POE over 4 wires (2 pair)

I’ll try to explain what I would do in that situation..
MT Gigabit PoE adapters work both ways - as injector and as well as splitter.
You can use 2 pairs to transmit power and data, but crimp connector to pins 4,5,7,8.
Recrimp both Gigabit PoE injectors (or build adapters - RJ45 jack ↔ RJ45 connector)

to map wires like this:
1->4
2->5
3->7
6->8

And replace far end GigaBit PoE adapter’s power plug gender (or make adapter)

I haven’t tried this, but it should work..