Yes, it's accurate. At its peak, the US was consuming almost five cords of wood per person. Meaning each American individual was consuming almost as much wood as an entire European household.

Americans burned so much wood because it was readily available and considered superior to the alternatives. For example, America has plentiful peat resources but even in regions where peat was readily available Americans preferred to burn wood. European peasants tried to burn wood or coal but often just couldn't afford it. They also had much more limited access to forests than Americans since land use was much more intensive and aristocratic in Europe. In contrast, Americans had a plentiful supply of wood. In fact, Americans still do: America has been exporting lumber and wood products basically its entire existence.

Other than that, it's mostly a matter of energy requirements and energy efficiency. You say your primary source of heat is wood. For a colonial, their only source of any form of power was burning wood. Candles and lanterns existed but were solely light sources. And they were relatively more expensive than wood. Not extremely expensive but more so. So they not only needed to heat their homes in winter but have fires going year round for cooking and light.

But the bigger issue is how they burned the wood. If you can heat your home with five to six cords then you are definitely not burning open fires. You probably have a furnace with a heat distribution system. Maybe you have room stoves. But the American colonists were living before the industrial revolution. Only wealthy homes could afford even relatively basic baffles. Most American homes would have been using open fires in fireplaces. Indeed, even many European aristocrats used them into the 19th century. This is hugely inefficient compared to more modern heating systems.

This was why the Franklin stove and other such innovations were such a big deal. The Franklin stove wasn't so much a technical innovation. The first patent on such technology was in the 16th century and Benjamin Franklin's contribution was fairly minor. But David Rittenhouse found a way to manufacture them relatively cheaply. This brought the price down to about twenty dollars. This was still a lot of money. It was something like a year and a half's wages for a common worker. But that was still significantly cheaper than it had been. Rittenhouse also combined it with novel financing which allowed them to be installed more widely.

Importantly, at that price it paid for itself in what we would today call energy efficiency. (Another big selling point was the lack of smoke and the more even distribution of heat.) They could cut a house's wood requirements to as much as a tenth of an open fire. (In reality, it appears colonial houses only decreased their wood use to a third to a fifth of the original. But they got significantly more power from this wood.) Rittenhouse and Franklin were also quite good at marketing this kind of innovation.

The introduction of these more efficient heaters freed up a lot of time spent chopping wood. And it meant that wood could either be put to other uses the land could be turned over to some other use. It was also much better at smoke management. That not only was more pleasant (breathing smoke is not fun) but made furnishings last longer and food cooked over it taste better. You could also have a more enclosed environment against the elements since less smoke needed to escape. This further helped with keeping heat.

Over the course of the 18th century they became normal in the United States. (It took longer to be adopted in Europe. This was partly due to the relative wealth of the American lower classes. And it was partly because of the lack of a Rittenhouse figure who focused on mass manufacture, distribution, and financing. Instead, stoves remained more ornate and expensive in Europe for some time.) They remained normal in most homes until the late 19th/20th century led to the utilities revolution. When homes got heat, air condition, electricity, etc then these wood systems became redundant.

As for how they got that much wood, they got it like how they got basically everything else. They made it themselves. It was normal for American farms to have acres of woodland attached to the house. (This was, by the way, a luxury compared to Europe where peasants had to negotiate with lords for the ability to take trees or fallen branches from the lord's forests. This is why Europe has such a big culture of alternate fuel sources.)

Prior to marketization, most households produced everything or almost everything they consumed. And they continued to produce much of what they consumed until the so called consumer culture of the 20th century. That is what consumer culture means: that you expect to be able to go to the store and buy all of your material needs. That your primary economic activity is selling your labor on the market to enable your consumption from the market. This is an extremely recent phenomenon.

Of course, marketization and consumerism came to different places in different times. There were wealthy people buying wood in 17th century Boston and New York. That's a sign of marketization, by the way, because the normal procedure would have been to hire people to maintain a forest and chop wood for you. That's what the whole forest warden system in Europe was. In order for people to buy chopped wood in a city market someone has to own forest land and maintain the trees. Then someone has to hire workers and go out to chop it down. Someone has to bring it into the city. And then someone has to bring it to a market and sell it for more than their costs. (I am skipping over a ton here. There has to be money. People have to supply and maintain the tools. People have to transport it to the final destination. This is all fantastically complicated for a product that is mere wood, let alone manufactured goods or services.)

Some more perspective and odd facts:

Is the 30-35 cords an accurate number?

It actually is a low estimate. The average consumption per home was more like 40 cords in pre-1750 America.

That seems like an absolute ton of wood.

More like 80 tons of wood (assuming the typical hardwood average of 4k lbs/cord). That's a lot of wood. With the dense Northeast American forests full of trees, this equaled about an acre of forest per home per year, which by the 18th century started to cause supply problems. Many landowners would leave 20 acres for a steady supply of wood, cutting about one a year and allowing it to regrow over the next 15-20 years. Some of our early laws protected the dwindling supply. The Pilgrams restricted wood exports, and William Penn stipulated, in 1681, that one acre shall be left wooded for every five cleared. In 1691, Massachusetts reserved certain trees for use as masts by the Royal Navy, and in 1700s the Navagation Acts prohibited the exportation of most lumber products to any other nations or their colonies, reserving those supplies for the massive Royal Navy as well (though lumber itself could be exported). America, to some degree, even owes its birth to the quest for logs. In the mid 1500s, England nearly finished depleting her forests. One man, Richard Hakluyt, petitioned to establish colonies in America and was one of the first members of what became the Virginia Company of London. In his open advocation for the investment, he named reviving England's "decayed" industries as a reason - meaning specifically wool, cloth, and perhaps most importantly, wood. In a second writting from Jan 5, 1607;

REASONS OR MOTIVES for the raising of a public stock to be employed for the peopling and discovering of such countries as may be found most convenient for the supply of those defects which this Realm of England most requires:

1. All kingdoms are maintained by rents or trade, but especially by the latter, which in maritime places flourishes the most by means of navigation.

2. The Realm of England is an island impossible to be otherwise fortified than by strong ships and able mariners, and is secluded from all corners with those of the main continent; therefore, fit abundance of vessels should be prepared to export and import merchandise.

3. The furniture of shipping consists in masts, cordage, pitch, tar, resin, and that of which England is by nature unprovided; at this present time it enjoys them only by the favor of a foreign country.

In a long list of reasons, it was placed at number three. One of the first things they sought to do was send lumber and lumber products to England. Its a part of what motivated the original investors, due to the enormous costs for those materials in London. In New-England the Pilgrams recorded their first payment to their investors, the Fortune was filled with wood and set sail for England, though the materials would never get there.

How did they possibly cut, buck, split, and stack that much?

The good old fashioned way, one swing at a time. Often neighbors would band together for clearing and much was done in the fall/early winter. Those more well to do, of course, paid or forced others to cut wood for them. At Jefferson's Monticello, as he began to increase his nail production in 1795, he ordered 23 cords cut for firewood and another 50 for charcoal with four men hired to do the work. In Sept of 1799 the total had increased; six men were hired to cut and split 200 cords of wood. In 1807 an order was placed, this time for over 180 cords - for the charcoal alone. One tactic used in the felling of trees was something learned from natives called "girdling" in which a band of bark is removed from the tree, causing it to die as it stood. Later, axe wielding colonists would come and fell the trees (which led to the development of American felling axes) and leave them in pieces about 4' in length - about as big of a log as a human can handle - and stacked them 4' high by 8' long, which was about as much as a horse could pull. Today we call a stack 4×4×8 a cord, a word that started in the early 17th century.

I can't see how that would cause that much extra burning of wood.

In a word? Inefficiency. Beyond cooking uses, open hearth fireplaces, what the vast majority of homes used for heat, are about 10% effecient. This means 90% of heat generated goes right up the chimney, and that heat escaping draws cold outside air through poorly sealed planks prevalent in their homes. As such the amount of fireplaces and wood burned was phenomenal. The first major reduction in consumption occured in the early 1740s, namely 1744 with Franklin's publication on his "Pennsylvania Fireplace" design. Having had it in use for several years already, the publication allowed the plans for the stove to be widely shared. Further, his refusal to patent the stove meant they could be had for the cost of manufacture alone, which in Philly was £5. Soon the pamphlet crossed the ocean and was translated to both Dutch and French, being widely applauded. Still, as pointed out, it would be others that later refined this unpatented design and increased its efficiency to what we know today as the "Franklin Stove." Others made similar comtributions, like the Rumford Fireplace of the late 18th century, which allowed options with a much higher efficiency than the basic open hearth design.