Sorry Elly, my mistake. 350 and 400 were both also transmission models of this era.
As for the starter problem, consider this: V8 engines almost always stop at one of 4 places in the engine’s rotation, give or take a few degrees. That’s because the engine will pretty much stop as one of the 8 cylinders comes up on compression. There are only 4 places on the crankshaft’s rotation that fill the bill. So the starter tries to begin engine movement at pretty much the same place on the flex plate frequently. If there were teeth missing, nothing would make the engine turn except someone moving the crankshaft by hand to make the starter engage a different place on the flexplate with no missing teeth.
If the starter was spinning without spinning the engine there are only a couple possibilities. First, the starter drive is failing. The starter drive, or bendix, is the gear at the front of the starter motor that engages the flexplate. It’s a lot like a ratchet. If the starter turns without spinning the motor the bendix is freewheeling, like a broken ratchet.
The second possibility is that the bendix tries to engage the flexplate but can’t. It will then spin anyway, and make a positively awful lot of noise. The answer to that would probably be to ADD a shim or two to the starter, rather than remove one, since removing the shim brings the bendix closer to the flexplate, and it’s already so close it can’t engage consistently.