I'm going to propose an alternate solution: consider switching to the Godox flash system, which uses big lithium rechargeable batteries. The battery is proprietary, so that's not so handy, but they're also not that expensive and easily available from major retailers.

These will generally give you more shots than a set of Eneloop batteries in a flash, but perhaps more importantly, if you need to swap, it's really easy and fast: none of this " managing about 50 batteries" — if you have three flashes and three backup batteries, that's just six, and each swap is just one out, one in. As you note, the transmitter battery isn't really a big issue and should last several sessions — and in the Godox case, you don't need a separate radio receiver as it's built in.

If you're going all-manual, the flash units with one battery cost around $140 plus $40 for spare batteries — so, $540 for three flashes and three spares, plus $46 more for the transmitter.

That's an almost-$600 outlay, which I know isn't trivial, but if you were already planning to add a ~$100 flash, $20 worth of new eneloops, and a $50 USB bank, plus whatever else needed to make that work, the real difference in price decreases. And having three back-up batteries may be overkill — especially if you're not always shooting at full power. All in all, it seems like it might be worthwhile for your sanity.

(For what it's worth, I've got exactly this setup, albeit with the older generation of Godox li-ion flashes and the 433mhz trigger system. In combination with a portable lightbox kit and some foldable lightstands, the whole thing definitely easily fits in two big bags.)