So, I tried this last night, and found some issues. I had de-tempered some 32g wire, and went with five wraps. After removing the picks, the thing sproinged a big, but I was able to manipulate it back into a reasonable shape, fed some thread through it, and put it in the head. The main problem I found was trying to get this coil to give a good or consistent resistance. When I first tested it, I was getting around 0.9 ohms, but manipulated it some more, and found that depending on how it was positioned, got anywhere from 0.9 to 2.8 ohms.
I assume that there are some miscellaneous shorts, either on the positive side, or coils touching. In the end, I just couldn't get it to hold a reasonable position consistently enough to make this usable.
Do you have any hints as to how to stabilize this in some way so that it doesn't touch other parts? When I'd simply wrapped some wick previously, the wick itself stabilized the shape and position, but am not finding a good way to do it when coiling, then threading.