Ammo should be properly carried over to the next level. If it doesn't it might be a bug.
And yes, you can just copy your files to move your project over to PRO version.
I've figured out the problem! Though I don't know how to solve it. It only happens when you set the weapon's magazine to 0 (to remove reloading). When you have reloading enabled, it starts your gun fully reloaded on the next level and keeps the correct total ammo. My guess is that when reloading is disabled, the total ammo and magazine ammo are read as the same thing by the engine, and sets your "magazine" to one stack, overwriting your total ammo.