Shimming drive side is a common practice when using a modern cartridge BB on a vintage crankset (like the Sugino AT above) that was designed for an asymmetric spindle. Of course, it just moves the crank to the right. If the BB is too short, you just transfer the problem from the drive side to the non-drive side.
Even Sir Sheldon recommends a spacer on the Sugino AT:
https://www.sheldonbrown.com/bbsize.html
I don't understand why the FSA would not work with a longer spindle BB. But the Shimano is a nice choice too.