So the engine is not original to the vehicle?
When replacing the motor, did you replace the flywheel with the one from your original motor or did you use the one it came with?
The cure would be to use the one from the original motor and then use your old camaro starter. It is very important to use a flywheel with the same amount of teeth, if it has a different amount YOU WILL have gear meshing issues not catching, grinding, sometimes starting perfectly while other times sounding like its missing. This is due to to incorrect # of teeth to match the flywheel to the starter.
The first step is to find out how many teeth the original part flywheel had if that's not the one mounted now count the teeth on the current flywheel, it should be either 168 tooth flywheel or 153 tooth flywheel.
The engine block doesn't matter if its from a camaro, blazer or chevy dump truck as long as the flywheel and starter have the proper amount of teeth to mesh. If that doesn't seem to be as much of an issue then you just need to add or remove starter shims until the starter teeth mesh with the flywheel teeth, NOT deeply but at about half way up the lead tooth. See proper gear meshing
Also make sure you did not put the flywheel on backward!!!
Also it may be a good turn flywheel and examine teeth for chipped or damaged teeth. SAFETY TIP:
Always remember to disconnect the battery when working with the starter. TIP:
Get a quality starter, not a part from the dirt cheap discount part store. Places like carry cheap **** that can cost you time and nerves. I once had a problem where I tried to by re-manufactured
starter, exchanged it 3 times, then went for new, exchanged it twice and then returned it and went to a more expensive quality supplier and got a far superior product that actually worked perfectly. Because the part is new or freshly re-manufactured
does not mean that it is a good part. The same goes for batteries, because you buy them new, sometimes they come DOA dead on arrival.This is what a starter shim looks like Here is another article on the topic that explains the issue pretty well.