My only question is would the rats be able to get to their food through the 1/4 inch stuff? That is the only reason I could see where the size of the mesh might possibly influence how they grow.

I haven't kept ASFs, so I don't know if they can escape through 1/2 inch mesh. Obviously, if they can that is what you would have to go with if you are going to build for them.

All of the 1/4 inch mesh I've been able to find locally is 23 gauge. Personally, I don't trust it with rats because it feels flimsy. But I haven't tried it to know if it works or not for them. I'm using 19 gauge in my rat boxes and so far so good, and I've seen them trying to gnaw out and it isn't working out for them.

I haven't had too much trouble cutting the 1/2" 19 gauge. I got myself a good heavy set of sidecutters and they go through the stuff pretty easy. I wouldn't want to try it with a cheap set, though.