I don't buy this story - P2 only briefly burped around GPStime 1291608000 which is around 8pm local time, which is when I was recovering the system.
Today. Jordan talked to Jon Feicht - apparently there is some kind of valve in the TP2 forepump, which only opens ~15-20 seconds after turning the pump on. So the loud sound I was hearing yesterday was just some transient phenomenon. So today morning at ~9am, we turned on TP2. Once again, PTP2 pressure hovered around 500 torr for about 15-20 seconds. Then it started to drop, although both Jordan and I felt that the time it took for the pressure to drop in the range 5 mtorr - 1 mtorr was unusually long. Jordan suspects some "soft-start" feature of the Turbo Pumps, which maybe spins up the pump in a more controlled way than usual after an event like a power failure. Maybe that explains why the pressure dropped so slowly? One thing is for sure - the TP2 controller displayed "TOO HIGH LOAD" yesterday when I tried the first restart (before migrating everything to the older UPS unit). This is what led me to interpret the loud sound on startup of TP2 to indicate some issue with the forepump - as it turns out, this is just the internal valve not being opened.
Anyway, we left TP2 on for a few hours, pumping only on the little volume between it and V4, and PTP2 remained stable at 20 mtorr. So we judged it's okay to open V4. For today, we will leave the system with both TP2 and TP3 backing TP1. Given the lack of any real evidence of a failure from TP2, I have no reason to believe there is elevated risk.
As for prioritising UPS swap - my opinion is that it's better to just replace the batteries in the UPS that has worked for years. We can run a parallel reliability test of the new UPS and once it has demonstrated stability for some reasonable time (>4 months), we can do the swap.
I was able to clear the FAULT indicator on the new UPS by running a "self-test". pressing and holding the "mute" button on the front panel initiates this test according to the manual, and if all is well, it will clear the FAULT indicator, which it did. I'm still not trusting this unit and have left all units powered by the old UPS.
Update 1100 Dec 11: The config remained stable overnight so today I reverted to the nominal config of TP3 pumping the annuli and TP2 backing TP1 which pumps the main volume (through the partially open RV2).
According to the Tripp Lite manual, the FAULT icon indicates "the battery-supported outlets are overloaded." The failure of the TP2 dry pump appears to have caused this. After the dry pump failure, the rising pressure in the TP2 foreline caused TP2's current draw to increase way above its normal operating range. Attachment 1 shows anomalously high TP2 current and foreline pressure in the minutes just before the failure. The critical system-wide failure is that this overloaded the UPS before overloading TP2's internal protection circuitry, which would have shut down the pump, triggering interlocks and auto-notifications.