Stock, the A is sorely challenged to run a modern auto.
Won't do you any good for the project, but there was an automatic epicyclic gear trans conversion for Model As in the early thirties. I've seen an ad for one in one of the old A books, and most of one back about 1960 at Meridian auto parts in Orange Co, CA. There was also a pre-selector conversion for stock Ford stickshifts. I've seen a couple at round-ups over the years. They work sort of like a Wilson, except are completely externally mounted. Those do require you push the clutch pedal though.

I ran a modified iron case GM hydro in a 45 Ford pickup but that was no stock engine. I have seen a fullhouse flathead V8-85 in a falcon ranchero about 30 years ago run Bonneville. I have no idea why.