Backfiring is a timing issue. Does this unit have the ECS system (no throttle cable- drive by wire)?
If you say the valve timing is spot on & the ignition timing is spot on- then I would suspect that the electronics are failing. I have found that when Toyota electronics begin to fail, they need a HUGE adjustment of the distributor (usually advanced) to get them to start, then backing off of the ignition timing to keep them running.
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