to answer your original question I have not seen this - My 782 was approaching 2000 hours when the connecting rod decided it did not belong in the crankcase. My father bought it new. my mother mowed 15 acres with it for many years then I used it for 8 years on 4 acres until the engine went, with the original starter still working.
this is the breakdown of your starter
as I understand your issue -starter works fine when the engine is cold
But on hot restarts, the fully extended Bendix is no longer close enough to the flywheel to engage.
there is no room in the starter motor for the armature to move the amount you are seeing without hitting the stator.
to me this means:
1. the bendix is too loose on the armature shaft and it has gone catawampus. This would seem odd to be predicated by heat of the engine - the starter should be relatively independent of the engine heat so this lack of gear engagement should happen hot or cold
2. wrong starter this too seems like it would cause problems hot or cold. If it is the wrong starter the flywheel teeth look very nice for that to be the case.
3. not mounted securely or properly - this could be heat related but I would not expect it to self correct after the engine cools - unless the mounting is cracked - separating with heat and closing back up when cool. I would think this would be visible or possibly even cause a leak. but the starter is held on by ears cast into the block so this is possible.
with any diagnosis of equipment the best question is what was the last thing you did before this started happening? start there and see if that is the cause
I guess my next question is, are you buying rebuilt starters? - your shop should able to tell you if the starter gear to armature shaft have excessive play. there should be almost no play. Still I dont know why engine heat would impact this.
I dont know if this helped but I hope so.