I can't see any harm in trying a a band-aid fix on the wire shielding for the humcanceller... I mean, worst-case it'll do what it was going to anyway, right? If it's me, I'm looking for a replacement right now while in rebuild mode. If it wasn't destroyed, and if they can find it, (both of which are pretty low-percentage) you are welcome to the one from my other Series bass that's at Alembic for pickup replacement (and some other stuff I forget...). My understanding is that they don't make much effort at saving those dummy-coils when replacing them. You should be able to get a replacement, and I would.
What you're describing about the trimpots doesn't sound good. You need those to work in order to dial out the hum. I can't think of a reason why it'd be worse with the 1/4" jack from the 5-pin... there shouldn't be any. Poor contact with shielding paint maybe?
I can't really help you sort out these electronic issues, as I am right much of a Wire Dunce. These guys are sharp on this stuff though. I'll try to put together a pictorial for filling and covering those screw holes... email on that coming later.
*regarding finish; not sure if it is even available to you in CA. but I use, and love Deft. They have recently changed the product name to ProLuxe, but they swear it's the same formula. It's an acrylic lacquer, and it's crystal clear... absolutely will not corrupt the natural color of the wood, but will definitely enhance it. Think: grain *pops* when this stuff seals it. But you have to get all that oil offa' there. Wipe it down with lacquer thinner first.