My truck when I got it had the 4.11 rear. A little slow in real life, I changed it out to good effect (the truck is light without a load) to a 3.54 - which I would recommend for ANY Model A - providing you have a strong engine.
The only SURE way to confirm which of the two original ratios you have is to block up one rear wheel and then using the crank, turn over the entire system starting at the engine end. Count the number of turns in at the crank versus the number of turns out at the wheel - then account for the fact that a differential will make the rear wheel turn twice as fast if you're only turning one wheel of the two.
However, and since you're talking about a commercial vehicle, check your torque tube on the rear axle. If it is "straight sided" for the rearmost 2/3rds of the tube, then you have a 3.78 rear. If it is tapered uniformly between transmission and punkin, then it's likely - but not assured - to be 4.11.
We've discussed this issue years ago on the old Ahooga site - and while I can't confirm this from others, it is what I found on my CCPU. It would make sense that Ford would need a way to tell the 3.78 axles from the 4.11 axles while being assembled to the chassis. A tapered torque tube would do that.
Good luck with that 150A. My third choice of Model A to own After my own 82A CCPU and the 76A RPU.
Charlie Bass, our distinguished ex Congressional Representative from NH owns a 150A. He tells stories of apple picking while standing on the roof of his.
Joe K