Just wanted to point something out here, that solid core wire you have will work just fine. Wire is wire. Cloth-wrapped wire is the same as PVC or anything else like that. The only place the casing makes a difference is in pickup wire, due to the difference in thickness of the casing that a coil will be physically different and have a different mag field as a result.
The only difference will be the resistance of the wire, which will still be no more than 2 ohms in the lengths for wiring a Jag. And stranded core wire is more flexible than solid core, but for the most part it won't make a difference.
When I rewired my Jag for series/parallel, I used solid core 22 gauge wire, mainly because thats what I had on hand. I measured the resisistance of it and compared it later to the same length of stranded core, the resistances were the same. The gauge doesn't matter much, 22 or 20 gauge will work fine. The resistance of 22 gauge and 20 gauge are extremely close. If you don't believe me, check out this table here, the resistance for 1000 ft of 22 gauge wire is 16.14 ohms, vs 10.15 ohms for 20 gauge. Divide those numbers by 1000 to get the resistance of 1ft of wire, and you will see that that for our purposes, it doesn't matter. For some good info on wire and what really matters much, check out http://www.tubetoneamps.com/productpages/wire/wire.htm
All that said, solid core can be harder to solder sometimes, because you can't wrap it around a lug as easily as stranded. But functionally it will be the same.
EDIT: After re-reading my post, something didn't sound right, so I just went and measured the resistance of 1ft of 22 gauge copper wire, stranded and solid core (I was bored).
The resistance for 1ft of 22 gauge is 4.5 ohms. For BOTH strand and solid core. So ignore that part above about dividing by 1000 from those ratings on that table, its a more complex formula for getting the resistance of a length of wire. I apologize for misinforming. I have a hang over headache and wasn't thinking clearly when I said that.
EDIT AGAIN, DAMMIT: I still wasn't satisfied, so I measured again. It is really hard to get accurate reading for that small of a resistance. According to this calculator 22 gauge wire has a resistance of 0.016 ohms per foot. So my original point was correct, divide the numbers on that first table for wire gauge by 1000 to get the resistance per foot. I'll just stop now.
