According to the United States Code, which has a special section for commemorative coins: “No coin issued under this subsection may bear the image of a living former or current President, or of any deceased former President during the 2-year period following the date of the death of that President.”
Archive article: https://archive.is/28sTn
That would be a nice thing to do. And beyond the cost of the engraver, it could be free almost. Just buy the coins modify them and uae them as part of your normal spending to get them back into circulation.
It worked for Where’s George. Coins don’t have serial numbers, though. There must be some way to put a unique identifier on each coin to gamify the fun