The initial diagnosis was just based on experience. The engine had all the symptoms of fuel starvation, no power, cutting out. When it cooled down, it ran OK. This did end up turning into quite a saga though.
The only pump available to me on a Friday night was a cheap O'Reilly 'import direct' pump. A pump motor and inlet 'sock'. I figured it would be good enough to get us 800 miles home and we were leaving the next day. So I bought that, a few basic tools and installed it in the parking lot of the hotel. Well, it turns out it was only able to last 600 miles. The car died entirely on the 15 South 45 miles north of Barstow (middle of nowhere). Even after it cooled down, it was a complete no-start, cranking only, no firing. A quick shot of ether in it's snout would fire it right up so I knew it was still a fuel issue. Tow to Barstow and began to doubt my initial diagnosis.
After an unplanned night's stay in Barstow, we found a mobile mechanic to come out in the morning and do a proper diagnosis. At that point the car would start but would not rev, would not drive, would idle only, any demand for power and it stumbled and died. The mechanic checked a lot of things the CAT, MAF sensor, but when he got to the fuel pressure test, it failed with 24 PSI fuel pressure at the rail and spec somewhere around 65. He pulled the fuel pump back out and there was no obvious issue with it, but it was certainly the issue.
The pump sits in a snap-together plastic housing that also includes the fuel gauge sender and the fuel pressure regulator. The newer models of Toyotas do not have fuel returns, the fuel line is pressurized by the in-tank pump and the regulator is also in the tank, so return fuel stays inside the tank. So it's possible the regulator was bad and not the pump, but it seems unlikely that a bad regulator would self-heal as the symptoms had been intermittent up to this point. So decided to put a full assembly into it, and way overpaid for the only full assembly available on a Sunday in Barstow and had to take an Uber ride 60 miles to Victorville to get it.
I put that thing in and the car ran normally again and just fine, fuel pressure was back up to spec, except... the new pump sounds like a blender on a smoothie setting. I can hear it driving down the freeway with the radio on. Mind you this thing was not cheap. $850 worth of not cheap for it, supposedly the same quality/build as OEM. Of course there was no Toyota dealer parts department open to get the real thing.
We drove it the rest of the way home with the whining pump and made it. I've already removed it and ordered an OEM pump assembly from Toyota, for only $500 so the AutoZone piece of crap is going back to where it came from and the Camry can sit in the drive until it arrives.
Failures on the road are difficult to deal with. I also learned that 2011 Camry 'Circuit Open Relay' is not a replaceable part. It is soldered into a motherboard inside of the fuse box under the hood. It's effectively a fuel pump relay and it cannot be replaced. You have to replace the entire fuse box assembly.
Next trip will be in the 80, the extra fuel cost will be worth it.