OH MY FREAKING DOG!!!
When I studied the original circuit in preparation for remounting it I noticed a couple of cables were coax.
So it turns out that the pups output a separate ground as well as a ground on the shield of said coax cable. I had just soldered the entire coax as one to the signal side of the balance pots. I did actually notice a little gunk but I had just switched solder, so I just assumed it was flux or something.
I hurriedly cut one off, stripped it properly and connected it straight to the amp. SOUND! It works.
The pup has a resistance of 7 k-ohm, which is much more reasonable.
This is by far the most embarrassing mistake I have ever made in DIY electronics. But Oh my I'm so happy at the same time and so is my daughter.
I can't do it right now but I will try and just wire it up correctly with the new preamp, and if that misbehaves (which it probably wont) I will install the old one.
A million thanks to everyone who wrote here. I don't think I would have discovered my error without you. I will report back if the new preamp turns out to be compatible or not.