1969 Chevy Corvette Starter won't disengage

Electrical problem
1969 Chevy Corvette V8 Two Wheel Drive Manual

I've had the same starter for last ten years - correct serial # and date code, rebuilt, very little use, and it spins the hi-compression 427 with ease. Lately it has taken to intermittently hanging up with the starter engaged - won't quit until I disconnect the battery. The car is equipped with a quick disconnect switch and the battery is behind the driver seat, so at least I can get to it quickly. I inspected the solenoid - the copper washer-type contact seemed a little burned, so I replaced the solenoid. Didn't fix the problem, so I installed a new ignition switch. Didn't fix the problem, so I installed a 1/32" shim between the block and the starter. Still didn't fix the problem. Any time the engine starts, there is no problem. But if the engine needs some cranking to clear it before it starts (usually about 30 minutes after a shutdown) the starter will hang up.
I've run out of things to consider. Any suggestions?