I am fully aware of the danger, this is not an average homemade pack and not my first time building HV packs (the previous ones were for Formula Hybrid and then Formula Electric cars, with all the requisite safety thingys).
Anyway, the pack will be fully isolated from the enclosed metal chassis, and the output of the inverter will be floating relative to output GND (which is bonded to chassis). It will have an embedded isolation monitor to shut off in case of an isolation failure. If someone grabs a live output while touching the GND, nothing happens, since, again, the phases are floating. The IMD will then shut the pack off due to isolation fault within a few seconds, to handle latent fault scenarios (not strictly necessary to handle only single faults). Obviously no GFCI is needed here either, there's nowhere for the current to leak.
Think of it less as a UPS and more like a very small Tesla/EV pack with an embedded non-isolated inverter with all the same safety functions. Anyway, the BMS cost will be way out of whack in this case no matter how it's done, but it's worth it for me because of the high-power (600W) embedded inverter, and having 98% efficiency (single-stage non-isolated) vs ~90% (48V-> boost to 200V -> invert to 120V AC) is a huge difference in the size and weight of the cooling system.
I keep coming back to the lingering feeling of needing balancing, at which point might as well have a full BMS setup with a stack of 14S monitors.