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The engine was kicking back and hard to pull. Investigation showed a bent flywheel key.
I replaced the flywheel and key with the same model number items.
With the new parts in place, the engine still kicks back and refuses to start.
I have checked the blade key, to make sure the blade is correctly attached to act as the additional load on the engine. It is attached and moves with the crankshaft.
.
What else could contribute to the kickback and not starting?
It still seems like an odd timing issue, but visible parts are where they should be.

Did you retorque the flywheel nut properly, if not you may have sheared the new flywheel key you installed.

Does this motor have the magnets inside the flywheel? Possible that one of them came loose and is out of place?

Jacks shows the craftsman number crossing to Tecumseh LV195EA-362011B,
Shows using a solid state ignition so probably no magnets under the flywheel.

Checked the flywheel nut and key - nut is tight, key is still intact.
This motor looks like it has the magnets mounted in the flywheel itself - in a wide part of the flywheel and spinning past the coild, mounted by the flywheel.

I did notice when checking the nut that it felt like there was a tiny bit of "slop" between the turning of the flywheel and any tension from the engine.
This is not my own mower, so I don't know how many times it might have hit things in its life. Would it be possible the "slop" means something not quite right inside the engine itself?