here's three I found earlier.

those are even better: plug-n-play.

Those atx power connectors are fairly difficult to find.

Well I have a handful laying around from stripping dead ATX motherboards for usable parts.

Sounds more like the job for some of the more exotic types of opto-couplers than transistors.

"somewhat beefy circuit"
How much current are planning to pass thru?

The load of the battery is a small boost converter module that's been slightly modified (removed the on-board LED and it's current limiting resistor + the USB plug AND added electrolytic capacitors on input & output)
And if I've estimated correctly (including the typical efficiency of a cheap boost converter circuit), then we're talking about 1 Ampere worst-case.

I'm currently in the process of finalizing a UPS-like circuit, where the off-grid energy storage is one single & large li-ion cell.
BUT I simply don't trust the cut-off circuit in protected li-ion batteries enough to blindly rely on them, so I'll need some advice on the simplest yet still efficient and somewhat beefy circuit that can simply cut-off the battery from the voltage converter when the voltage output of the cell reaches 3.15 volt and lower.
I've already understood that I'll need a mosfet for that + either a zener diode + a resistor OR a voltage divider bridge consisting of a few beefy resistors.
But after that I'm completely blank.

Thanks in advance.