Bill, sorry to hear of your starter troubles. A couple of ideas:
1. take the failed starter out and try to inspect the ring gear very closely. Get a proper inspection light and one of those small extendable mirrors and check it out closely looking for broken teeth (turn the engine through 360 degrees) and wear spots.
2. Depending on the type of starter you have, take the starter apart and merely bolt up the face to the block - see if you can extend the starter gear and "feel" if engages with the ring gear without the starter gear being cocked to one side or binding. You may just have some misalignment but it sounds to me like you have either a) broken/missing ring gear teeth in a position of common repose for the engine (low compression), or b) misalignment to the extent that the starter gear is not actually engaging the ring gear.
It'll become clear with some more inspection and monkeying around with it - don't give up!