Hi Ed,
I think Lindy Fralin is your best bet in this situation. Lindy has done custom rewinds for years. PRS has used his pickups in the past, as well. Lindy's own pickups are fantastic (my favorite 'boutique' pickups...and less expensive than PRS pickups). Lindy and his staff are super attentive and very friendly (I've been there a number of times). They can even replace or change lead wires, if you are looking for another switching setup. They may also find the cut/nick and repair the wire on the bobbin(s). I recommend you call or email the shop (
https://www.fralinpickups.com/). In addition to buying pickups from Lindy, I've also had them repair and/or modify pickups, too. Their work was first-rate.
There are a couple things in your favor: 1) the Dragon II is a time-honored pickup, making it more likely that its construction and winding are well-known and understood by folks such as Lindy; 2) having the Bass pickup may help with identifying wire sizes; 3) I have technical information for the Dragon IIs that can help you nail the materials-side, leaving Lindy to determine the wind pattern (which they can do when disassembling).
Luckily, there is more information on the older pickups. PRS is notorious for not discussing even mundane material aspects of its pickups that high-end boutique builders either share or post outright on their websites. (IMHO, having the grocery list of ingredients means little, how the ingredients are assembled...then again, I'm not the one trying to sell $500 pickups).
Note the wire used on the Dragon Treble is very thin...it allows more winds on the bobbin with which you can increase pickup resistance. The downside is thinner wire is more fragile. The firs thing they will do is separate the bobbins and test each coil independently for continuity. It is unlikely both coils are shot. If the wire is broken along an exterior wind, they may simply unwind a bit, cut away the broken section, test for continuity, and then reassemble. If they remove a few winds, the difference in output (from 8000 to 7950) would be minimal. However, if the broken wire is deeper within the winds, and requires more extensive unwinding, they will almost certainly rewind the bobbin with new wire. The old 44AWG wire is very thin and more fragile from oxidation and age, making it very likely to snap during a rewind. Not worth the headache. If they do rewind the bobbin, you would then need to decide on whether the rewind the other bobbin as well or keep it stock. Personally, I think you might as well do both bobbins, given the age and fragility of the wire...if one bobbin failed, it might only be a matter of time before the other fails, too. Better off doing it right the time and ensuring your pickups last another twenty years.
DRAGON I - Treble
Res: 19.0 kΩ
Wire: 44SP (44AWG, copper, poly-nylon coated)
Winds: 8000
Polescrews: #5-40, steel alloy (prob 1018 or 1022), length varies by model (PRS avg is 0.70"-0.75")
Slugs: CR5 (cold rolled steel)
Mag: Ceramic
Machine: Wound on the "Artist" machine
Dragon I - Bass
Res: 8.0 kΩ
Wire: 42SP (42AWG)
Winds: 5550
Polescrews: #5-40
Slugs: CR5
Mag: Alnico 4
Machine: Wound on the "42" machine
