Have you been coiling it up using the “normal” over/under technique you’d use with your good XLR cables? If not, you might have “set” the cable with a twist. What works with some XLR cables that have been mistreated (coiled “over the elbow” style, which is a bad thing to do) is to stretch them out in the sun to heat them up and “relax” them. I’ve read of people draping them across their roof for a few days and letting them “bake” in the sun. Then you coil them over/under to “train them” and they can be deployed flat again without the spiral looping (foot grabbers) that “over the elbow” creates.
The same may work with your lav. cable, IDK. Might be worth a try. I do over/under with my OST lavs (which feels silly for a meter of cable, but it can’t hurt) and I don’t have the problem you’re describing.
As to mounting, you could try making a (strain relief) loop underneath the mic, and twist the cable in the loop to make the mic head go where you want. Then tape that loop with your twist down with gaff tape or micropore medical tape (if to skin) to hold that twist in place.
Another alternative might be to tape the mic head itself, using something like the Rycote Undercovers. This might preserve the orientation you want, IDK.