Wow, brave stuff indeed.I must admit I wouldn't rewind a pickup with it's original wire especially if it's been potted, sure you're going to break up the capacitance but you'll never get it back on tight enough by hand without breaking it as the wax is going to stiffen the wire right up.New winding wire is expensive and very hard to buy in 'small' spools.......the smallest we use is 4 - 5lbs and even then you're looking at over £100 for plain enamel...........solderable polynylon is cheaper but comes on huge 5-6 kg spools usually-enough to make ALOT of pickups but still going to cost several hundred pounds.
A rewind can make an old p/up sound alot better in a number of ways-you can alter the wire gauge, the wire type, the number of turns and the winding pattern.A quicker method than sitting there wrapping a bobbin by hand is to find something to rotate the bobbin for you whilst you feed the wire on between your fingers-you'll have better control over the winding pattern and can control the tension too.People have made winders from all sorts of things-old record players,drills........sewing machines are a favourite.At the end of the day it's whatever suits the person doing the winder-there's no right or wrong so long as you're controlling the wire going onto the bobbin and govern the tension,wind pattern and no. of turns.