I've forgotten who the OP was, but this has gotten SO completely out of
hand.

I've had the exact same issue before in a Ford truck. The problem was a
bad starter solonoid (the part mounted to the starter.) Solution:
replace the starter motor with the highest quality part you can find.
Avoid rebuilt if you can. If you must buy rebuilt, but it from the
dealer. Most aftermarket rebuilt parts are JUNK and should be avoided.