There is a transcribed compilation of recipes in A Colonial Plantation Cookbook: The Receipt Book of Harriott Pinckney Horry, 1770, which includes recipes collected by Harriott and her mother, Eliza Lucas Pinckney, on a South Carolina plantation in the 18th century. If you are interested in the topic of culinary history, it's well worth a read.

One notable feature is that the recipes do not typically include quantities for the ingredients, however pepper was a common feature in many of them (the digital copy on Gale Group indicates 61 hits for the search term "pepper" in the 349 book). Google Books has an excerpt from the book as well. Example (emphasis added):

##To Dobe a Rump of Beef
Bone it and lard it with Bacon, Season it with Sweet herbs, Challots, Pepper, and Salt, Put it into your Pot (with just water enough to cover it) with Carrotts, Turnips, Onions, and whole Pepper, cloves and Mace; let it stew over a slow fire for three hours till tender, then make a good Sauce with rich gravey, Morrells, Truffles and Mushrooms over it.

Similarly:

To make a good Gravy

Take a peice [sic] of lean Beef cut in thin Peices put a peice of Butter in Your Stew Pan and fry it Brown but take care it does not Burn. Season it with Pepper, Salt, Mace and Cloves; when it becomes a little Brown thro' in a little Strong broth made of some Beef or Veal Bones, a Couple of Anchovies, and a Gill of Claret, boil it up and set it by for any use in the Savory way of Cooking.

Now this does not in any way substantiate the claim that the use of extreme amounts of pepper, as you put it, was historically accurate, but it does suggest that pepper and other spices were available, at least for the wife of a plantation owner. It should be noted that Harriott was well-travelled in both southern and northern states, and that "the recipes are largely of upper-class Anglo-American origin, reflecting her aristocratic English upbringing" (Caroline Banks).

Sources:

• A Colonial Plantation Cookbook: The Receipt Book of Harriott Pinckney Horry, 1770, edited with an introduction by Richard J. Hooker, 1984.
• Review of the above work by N. Caroline Banks, The North Carolina Historical Review, Vol. 62, No. 3 (JULY 1985), pp. 358-359.

Problematically defining "frontier" as 19th century westward expansion:

19th century cookbooks were starting to incorporate measurements (even late 18th century ones have a few), but not always in the case of peripheral ingredients like salt and pepper. Additionally, they were published in cities--in the U.S., above all in Boston, for whatever reason--and access to ingredients especially while traveling west would have been far more limited, like /u/Oklahomasurfin suggested.

From supply lists in publications like the 1845 Emigrant's Guide to California, we see that a group of 1-3 people traveling from Missouri to California was advised to take 25 pounds of "salt and pepper." This sounds more promising than it is: Brigham Young's suggested supply list was calculated to be .04 oz pepper per person per day, whereas salt was .6 oz, ten times as much. .04 ounces is about a quarter teaspoon.

Obviously that number reflects the need to carry as little weight as possible on the journey. (And you are packing, according to the Emigrant's Guide, some 600 pounds of bacon, so.)

What is apparent from the supply lists and from travel diaries like Thomas Farnham is that black pepper was basically the only spice that pioneers were encouraged to buy in useful quantities. There is some evidence to suggest that more established frontierswomen took advantage of this. Helen Mar Kimball Whitney in Utah mentions obtaining boxes of pepper from the general store (but not other spices), as well as receiving a gift of storage jars for salt and pepper. Catherine Parr Strickland Traill, living in what she described as "the Back Woods of Canada," wrote in an 1832 letter:

What think you of a rice pudding seasoned plentifully with pepper, mustard, and, maybe, a little rappee or prince's mixture by way of sauce? I think the recipe would cut quite a figure in Cook's Oracle [contemporary cookbook] under the original title of"bush pudding."

"Seasoned plentifully" is the best reference I've seen to the significant use (overuse, perhaps?) of black pepper in established frontier cooking, as opposed to wagon trains en route. (Traill describes her cellar of "rice, sugar, currants, and mustard all jumbled together.")

Recipes from the era also tend to feature cayenne pepper, and diaries from Mormon women in the west mention it meaning they had access once living there. But they mostly reference using it in tea, medicinally.