I don’t know how everyone else feels about conductive thread, but I think it does a terrible job as wires. I’m lazy, do not want to hand stitch and do not want to coat the fraying fibers to prevent shorting. As part of a dress with embedded piezo transducers I’m working on, I did some explorations with how to make non-stretchy conductive fabric still stretch by cutting geometric patterns in with a laser cutter.
The general idea is to take conductive non-stretch fabric, iron on paper-backed applique glue, laser cut the paper side and iron the traces onto your stretchy target. If you want to do this too, I made an instructable here. (Link to pdf version in case)
As you can see, some work better than others.