So you had an engine that kept blowing crankshaft seals and to replace it you bought a used engine from someone who stated it "ran great but keeps blowing head gaskets..." I am not sure I would label an engine that keeps blowing head gaskets as a "great runner" but let me leave that for another discussion.
Common issues with the FH721 and related series engines is overheating due to clogged or plugged cooling systems, the problems associated with overheating (such as warped heads) and loose valve guides which can result in bent pushrods, blown head gaskets and so on.
Granted, this wouldn't cause it to die like it was shut off ...
If you want to go further into the overheating discussion I can do so, but it relates more to a mower that struggles under load... It will die if you push it and engaging a PTO will certainly do that, but if you disengage immediately it should recover even if sluggishly which would lead me to further search in the areas of overheating due to crud buildup and loose valve guides and warped heads and such... But again even with a warped head it would still run warmed up, it just won't run good.
So perhaps the issue is electrical, perhaps a wire is shorting out against the frame someplace but then wouldn't it do the same when cold? Might be worth looking underneath at the clutch connector... If that comes loose or if it has 3 wires and (I think) the ground wire is disconnected then it will kill the mower when engaging the clutch but also when moving the stick(s) because of the logic circuitry, still odd that it won't do it when it's cold...
Which leads me back to the ignition coils.
You stated you replaced these, if I recall correctly.