I had the honour of attending a lecture by Dr. William Harris on Feb 26th, 2015 at Carleton University in Ottawa, Canada, where Dr. Harris addressed almost this exact question. I have found my notes I took from this lecture, and if this sub will allow it, I would like to share some of what I can recall from this talk. I am not an expert on this topic, but I hope I can help provide some information.

The issue with a purchase as large as the one mentioned is, as you have realized, that the physical act of moving that much money is not only prohibitive, but also dangerous and difficult to store. The average weight of a Roman sesterces is known to be approx. 3.54g each. Quick math shows that a payment of 3.5 million sesterces would weigh around 12.39 metric TONS of coin and bullion. Even making an adjustment for coins of larger denomination (which were often also made of gold, so that probably wouldn't help matters), that amount of money would be a serious undertaking for a modern shipping or security company, not to mention one of the Roman era. Not only would you need to feed the wagon train to transport it, you would also need to pay the people needed to drive that train and also guards to guard both the bullion and your personnel. Moving that much money very quickly moves into the realm of the absurd.

The Romans had recognized this, and created systems to allow more fluid monetary transactions. According to Dr. Harris, the primary method large payments of money were made through the use of a system that would look very familiar to someone living today: through equity, credit, and credit transfer. See, for example, another purchase made by another Roman named Canius mentioned in "De Officiis" (Book II, 3.59)[Emphasis is mine]:

"Pray, Pythius," said Canius thereupon, "what does this mean? — all these fish? — all these boats?"

"No wonder," answered Pythius; "this is where all the fish in Syracuse are; here is where the fresh water comes from; the fishermen cannot get along without this estate."

Inflamed with desire for it, Canius insisted upon Pythius's selling it to him. At first he demurred. To make a long story short, Canius gained his point. The man was rich, and, in his desire to own the country seat, he paid for it all that Pythius asked; and he bought the entire equipment, too. Pythius entered the amount upon his ledger and completed the transfer. The next day Canius invited his friends; he came early himself. Not so much as a thole-pin was in sight. He asked his next-door neighbour whether it was a fishermen's holiday, for not a sign of them did he see.

"Not so far as I know," said he; "but none are in the habit of fishing here. And so I could not make out what was the matter yesterday."

Poor Canius gets duped in this story, but the point is that this is a first hand account of how the purchase of house is being made, through the use of a ledger and credit system. Certificates of credit were called "Nomina", and were kept in ledgers like the one described above. Ledgers or books of "Names" are mentioned as well in accounts of the Jewish Revolts when the Zealots burn the roman storehouses which they kept the "Names" (or Nomina) of the oppressed. Harris suggested these would likely have represented credit houses which, the act of attacking them an attempt at economic emancipation by the Zealots. At Pompeii, no large stores of ingots or bullion were found in the buried city, the absence of which would have been conspicuous in an affluent coastal trading city if the primary form of exchange was through physical money. Bullion would generally be reserved for emergencies, fast payment, or financial dealings with outside peoples. One humorous story told by Dr. Harris was of a Roman senator obsessed with making sure that the gold he would need to bring with him to his new African estate would be safe travelling across the Mediterranean (heavy, coin laden ships tend to sink...). He apparently tested the idea of using strong boxes affixed with cork and blown glass floaters to prevent them from sinking in the event of a shipwreck. (I wish I could remember the name, it's not in my notes, I may have been laughing at the description more than writing..) EDIT: u/sunagainstgold has kindly pointed out that I am likely wrongly remembering a situation involving Cato the Younger, and has the relevant passage below.

Trading by credit was not limited to a one to one arrangement between the debtor or creditor either. It was also possible to pay through "Delagatio", by which you could pay your debts by offering debts owed to you of equal or a negotiated value. To paraphrase Dr. Harris, you "paid your loans with loans you were never paid". All Nomina seemed to be negotiable to some extent, as many creditors preferred to be paid a portion of what they were owed if they felt the debtor might not pay at all otherwise. Credit markets existed as well, Caesar is described as passing laws to restrict the credit market and predatory money lenders (Cassius Dio "Roman History", Book 41.37-38):

Having obtained this, he at once instituted an important and necessary reform. Those who had lent money, it seems, being now in need of large sums because of the civil strife and the wars, were collecting their loans most relentlessly, and many of the debtors for the same reasons were unable to pay back anything, even if they wished to do so, since they did not find it easy to sell anything or to borrow more. Hence their dealing with each other were marked by much deceit and fraud, and there was fear that they might go to the point of accomplishing some fatal mischief. To be sure, the rate of interest had been lowered even before this time by some of the tribunes; but since payment was not secured even thus, but instead the one class was ready to forfeit its securities, while the other demanded back its principal in cash, Caesar now came to the aid of both so far as he could. He ordered that securities should have a fixed valuation according to their worth, and he provided that arbiters for this purpose should be allotted to persons involved in such a dispute.

Since also many were said to possess much wealth but to be concealing it all, he forbade any one to possess more than sixty thousand sesterces in silver or gold; and he claimed he was not enacting this law himself, but was simply renewing a measure introduced on some previous occasion. His object was either that those who were owing money should pay back a part of their debt to the lenders and the latter should lend to such as needed, or else that the well-to‑do might become known and none of them should keep his wealth all together, for fear some rebellion might be set afoot during his absence. When the populace, elated at this, demanded also that rewards should be offered to slaves for information against their masters, he refused to add such a clause to the law, and furthermore invoked dire destruction upon himself if he should ever trust a slave when speaking against his master.

Monetary reform like this actually happens a number of times throughout Roman history as their economy outgrows the systems it is built on (or collapses under its own weight) but that's a topic for another time. (See the reforms of Diocletian and as well as earlier in 130AD when small denomination coins were removed from circulation)

The TL:DR of your question is somewhat simple: the Romans avoided the logistical nightmare of moving around tons of roman coins and bullion by not using it for big purchases. Instead, systems of credit called "Nomina" were used inter-personally as well as through credit markets to move money around ancient Rome. It is suspected that much of the tax revenue from places like Syria were paid to Rome in this way, which begs the question what the local governors did with all that "idle" currency. Dr Harris did not have an answer for this, but surmised they probably quietly pocketed it or used it to pay local debts.

EDIT: Forgot my citation. tsk tsk (Chicago)

Dr. Harris, William. "Roman Money: Problems, Solutions, and More Problems." Lecture, The Faculty of Arts and Social Sciences and the Greek and Roman Studies Lecture Series from Carleton University, Ottawa, Ontario, Canada, February 26, 2017

Link to event page @ Carleton: https://carleton.ca/grs/2015/upcoming-lecture-understanding-roman-money-problems-solutions-problems/

Please see here, with some reckoning errors included.

What's the conversion on that to modern-day U.S.?

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