Having seen that reduction is size I thought it might actually still be the shielded wire. So I chopped it and carefully removed some insulation with a scalpel. It is shielded wire. Not sure why someone decided to double up the ground, but I think I can return to my original plan now.

 

If you had a double ground, that is probably your problem. The shielded wire must only be gounded at one end, for reasons I do not understand, but I know it is important.