These "remote diagnostic" exercises are always interesting. So I've been following the discussion. I usually side with Jonathan on these, based on his extensive experience (and he's usually correct) but I'm curious what about the symptoms points to valves?
The tractor ran, then something changed and now it won't run. It backfires, so that sounds like timing or valve problem. Is it "backfiring" out the carb or is it "backfiring" out the muffler?
How could the valves go out of adjustment all of a sudden? so much so that now it won't start.
Blown head gasket shouldn't cause it to not start (usually) and doesn't account for the backfiring.
To me, it's unlikely the valves went out of adjustment. All of a sudden. I guess they could start sticking all of a sudden, so that's a possibility, but the OP watched them operate, and they seemed to be OK.
I'm thinking it's a timing issue. Since there is good spark, I'd be double checking the static timing to be sure it hasn't changed. timing can go out of adjustment if the points are loose...you'd still get spark, it would/could backfire, but probably would not start if off enough.
That's my vote. (sorry, Johathan).
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