It's too short to shield properly. Having such noise issues already, I'm not going to chance it.
The Bartolini MK1's are not a full, dual-bar humbucker. The pickups are only magnetic on their top right and bottom left. Opposite polarities, so each MK1 is essentially like the two staggered pickups in a Fender Precision Bass, but packaged in one homogeneous "soapbar."
They are significantly lighter than the replacement BC5's going into it, which are definitely full-width humbuckers. The MK1's measured around 6.5k Ohms, and given that there is essentially only half the wire in there as opposed to a BC5, I'm guessing that the MK1's are connected internally in series. The BC5's measure about 15.5k in series.
Interestingly, I see a piece of copper tape on the bottom edge on both MK1's. Unsure what that goes to internally but I get 56 ohms to ground on one and 220 ohms on the other.
I just checked the MK1's again very carefully. The upper magnetic area is only for the D and G strings. The lower magnetic area is for the B, E, and A strings. Unless some very precision assembly was done, this could be a problem for hum cancellation due to unequal winding size. It is the very nature of the humbucking process (two identical coils, of opposite magnetic polarity, connected together in series or parallel) which reject induced noise. Any change in that relationship (magnetic, electrical, spatial, or otherwise) can affect the noise rejection ability. Maybe the damaged lead wasn't the biggest culprit in my noise issue?
In case anyone else reads this and is looking to replace their MK1's... the BC5's are a close fit, but the mounting holes do not line up. (Three-hole instead of two, and the one single hole is not in exactly the same place. So I'm waiting for two filled-in holes to dry before drilling all new ones.