I have a thought but it may not work. I don't know much about the AA pickups and was wondering if there is one made that would carry an A-Coupe on a flatbed or do they just not have the carrying capacity for that?
The Double A has plenty of carrying capacity, --- 1.5 tons, you would need the 157 inch wheel base, I am not sure how long the bed is?, would look pretty good carry an A, somewhat slow for anything on long trips.
I've seen AA's with both crank and hydraulic tilt beds. Saw one driving through Fort Worth that was was carrying a coupe. Unfortunately I was heading in the opposite direction and couldn't see what setup he was using. The tilt bed was a popular option throughout the mid and southern states for grain hauling. Go for it!
I'm pretty sure the earliest you could get a 157wb on duals was the 1930 model year. Prior to that they had aftermarket frame extensions and tag axle setups. Of course those accessories remained available for the later years and BBs also, but Ford began offering more choices as the years went on.