[Kevin in NJ]

Not sure of all the mixes of parts. Honestly I am pretty sure if you just rebuild the A brakes properly everything will be great. Truthfully brake rebuilding, any year, requires special tools. Here is where you are WAY better off paying someone to just build up a set of original brakes properly centered and shoes matched to the drums.

Now for a brake technology perspective on the Fords.

Really the only difference from 31 to 32 is the size of the drums. They make have played with the braking ratios front to rear. Honestly, I have not found fact based proof of what the brake ratio is on the A or the 32. People are just making assumptions based on the brake setup, but that I do not believe is proof. (keep mind I am not saying they are wrong, just I have not found evidence to prove any statements)

As they headed to late 36 they started doing changes to increase the mechanical brake floating. The wedges got bigger holes and they did a mushroom shape adjuster pin.
The pin change allowed more vertical movement of the shoes, but not side to side at the adjuster end.
The best brake design was from late 36 where they changed over to the floating adjuster. Now the brakes could float side to side. This is the bases Flathead Teds contraption. Unfortunately his design is more of a kludge in my view point requiring the external lock nut.
In 37 they kept the rods for the brakes but in 38 they went to cables. The cables are a problem in that they stretch.
In 39 they went to juice brakes. We had a 39, you do not want juice brakes as they are always trying to fail in the early design.

One of Ford problems I believe was that he was trying to keep in own design brakes. He did not want to pay royalties for using a technology. He kept slotted screws longer even though production labor cost were higher just because he did not want to pay to use the Philips screw.

As for braking, the tires are another consideration. The A brakes work great on the A with the original type tires. The real limiting factor in stopping the A is the tire to the road. If you improve the A brakes you do not do anything but make so you can skid the tires faster. That is just wasted effort. You must switch to different tires if you want better stopping.

In the end, properly rebuilding the A brakes is not cheap, easy or fast. To many want cheap easy fast repairs so they try everything but what is known to always work- rebuilding it back to factory.

If you want to learn more about the progression of Ford braking systems you need to read some of the early V8 service bulletins. By the way, the first few years of the V8 bulletins have A info too. I think that is missed by most people.