Per Matt's other post (from 2007!) the other pole is being used for some sort of variax setup.
The only other thought I had was to wire the Bridge HB (or the neck, your choice) as a std series-connected HB, and treat the other HB as if it were 2 SCs. IOW, coil #1 hot goes to lug #1, coil#2 hot goes to lug 3, Coil#3 hot goes to lug 5. Coil 4 hot joins coil 3 neg, coil 4 neg is grounded, as are the neg leads from 1 and 2 coils.
This would give:
1) Coil 1 2) Coil 1 + Coil 2 (neck parallel HB) 3) Coil 2 4) 2 + (3 X 4) 5) 3 X 4 (Br. series HB)
Whether this is more "useful" or more "standard" I leave to you. I was thinking this would be just like a HSS set-up, but then I remembered most of those schemes split the Br. HB at position 4 (by using the other pole of the switch, which you ruled out.)