Update: It happened again!
Dealer didn't want to promise repair would be covered under my ToyotaCARE Platinum plan (I have 59K miles). Wanted to charge me a minimum $42 to diagnose, then they'd ask the ToyotaCARE people if they'd be willing to fix, pretty please (the ToyotaCARE contract specifically includes relays AND the fuel tank/fuel pump).
After carefully reviewing the symptoms, wife and I decided to fix it ourselves. We came to the conclusion the only logical problem that could explain the behavior was the Circuit Opening Relay (why they call a normally-open relay an "Opening" relay is beyond me). This conclusion was based on the fact that the VIN of the car is too high for the ECM to be the culprit, and the symptoms (non-start on first try only, then runs fine) didn't support the fuel tank/pump theory. Also, the coolant temperature according to my scan tool was too high for it to be the ECM.
The dealer wanted $60+ for the relay (90987-02012), I found a GP-Sorensen brand equivalent part (41-5154) for $18.99 at AutoZone. This is a very ordinary SPST, normally open 12v relay. There are four or five identical parts in the same box, controlling fans and the horn, among other things. AutoZone lists this as a normally stocked part at their stores, though the first store I visited could not find theirs (the computer said they had one).
It's literally a five-minute repair, you open the fuse/relay box under the hood, pop out the old relay, and pop in the new one. When I tested the old relay it seemed to work fine, but since the problem was intermittent anyway I figured it was cheap insurance. Since the deductable on the extended warranty is $50 I figured this was the cheapest solution.
I'm holding on to the original relay and if this does not fix the problem I'll drop the old one back in and reschedule with the dealer service department.