A heady mixture of incompetence and using inappropriate components has resulted in some disappointingly untidy heater wiring.
The first mistake I made was not twisting the wire enough. When a pair of wires is properly twisted it has a certain feel to it and acts like a single piece of wire. In the first couple of attempts, I couldn't get the teflon wire to this level of twistedness, mainly because it kept slipping out of the drill! This meant that the pair of wires looks slightly irregular and untidy, and it came untwisted easily when I was working with it.
The second mistake was using teflon wire at all. It's an absolute pain to get it to stay in position when you bend it. I'm going to have to work out a way to secure it to the chassis at strategic points.
For the last run, I actually managed to clamp the wire in the drill properly and got a decent twist. The question is - do I go back and re-do the whole lot? Or do I let it annoy me forever (until I forget about it)?