I had a starter once that would not engage.
After taking measurements of the travel and proximity to the flywheel, I determined it had enough travel.
I then proceeded to shim each corner with about a .030 thousandth washer, one at a time.
It ultimately worked on the 4th try with a washer tipping it up and in from the bottom outside corner.
Either the casting was a bit off on the face or the inside alignment of the gear and armature were slightly off, probably a machining issue with the locating holes for the shafts on either end that hold the armature and gear.
At any rate it was an OEM Ford starter, identical in appearance to the one that came off the tractor, that should have lined up "out of the box" but did not.
I never had an issue with it once I got it to engage with the shim in place.
Good luck and let us know what you find out.