Look folks, here's the deal.
Power went out and the batteries kicked in. It lasted a while so the batteries drained to zero. Power came back on and the batteries started to charge. Computers started back up but peak load with all the machines and the battery charge causes the GFCI to flip. So I had to stop everything, charge the batteries, then bring everything online progressively to keep the lights on.
TODO: I need to run a dedicated 20A or tweak boot BIOS settings to prevent peak overload