The premise has big problems.

First, the dispute arose over some issues not limited to the wealthy; the colonies being taxed to pay the costs for the new acquisition of Canada, and the Proclamation of 1763 that had severely limited the westward colonial expansion into the Native Nations. Second, to say "engineered" implies control. The gradual escalation of the dispute was not started and managed by a unified colonial government, with a firm purpose. The various colonial legislatures were driven by the dispute to begin communicating with each other ( committees of correspondence) and finally created a Continental Congress that could meet and debate what to do next. Third, there were plenty of popular events in the escalating dispute that were completely outside of the control of the legislatures- the famous Powder Alarm of Boston in 1774, for example, in which the removal of gunpowder from an armory by the British Army sparked panic and the forming of an armed mob. Lastly, even as the Congress convened and debated, there was no unified vision of a goal. Opinions were divided, even to the end: the Olive Branch Petition of the pacifists like John Dickinson arrived in London at the end of August 1775. And even if the Congress had been unified, the dispute was not one-sided: the British -especially the King- adopted harsher and harsher measures in response that very much helped to drive the unrest. When the Olive Branch Petition was officially presented to the King ( though not read by him), he had already proclaimed the colonies to be in rebellion and military force was to be used to suppress it. So, you really can't say that the colonial wealthy elite started the conflict.

Some of the wealthy colonists did take try to take advantage of the War once it was underway to advance their economic interests. The wealthy colonial elite was very much in control of the Congress, and there was a great deal of materiél that had to be obtained to supply the War. Some came out richer, as a result: Robert Morris and his group of merchants. However, many merchants found that the patriots didn't want to pay their bills, or were suspicious of the amounts. At the end some merchants like Silas Deane and Oliver Pollock found themselves ruined, or sitting on large piles of seemingly valueless promissory notes. And even Morris, at the center of Continental finances, would come to grief shortly after the War was over.

One of the key drivers of the start of the dispute was that desire for more land to the west, and it continued to be important. And that motivated many of all classes, from slave-holding southern planters like Washington to poor hill farmers in Pennsylvania. Whether the lower classes would get their new lands, or discover they had already been claimed by wealthy land speculators, though...that would be a matter for the years after the War.