Welcome to the Forum!
Your Single coil expertise will be good to have here.
Sounds like your pickup could be out of phase.
Are both Coils wound the same direction, and the two finish leads tied together.
Not sure what your particular bobbins look like?
Is it possible one got flipped over, after they were built.
If it is a phase issue, all you need to do with the 4 wire hookup is reverse one coil, provided you wired out all 4 wires.
with 4 wire just tie a start & finish together.
Check on that, and please let us know what you find.