I've had great success removing old polyurethane coatings on nylon by just washing the items in a standard washing machine on normal settings using regular powdered detergent. Wash them by themselves as the old coating comes off in innumerable bits. Afterwards you have to run an abbreviated wash cycle in the empty washer to get rid of it all.
In the two or three cases I've done this a single wash removed all the old coating, with nothing hanging on and coming off slowly over the next decade. On the other hand, I had one tent rainfly whose coating became sticky, and no amount of washing seems to get it off. I will recoat over the old (still sticky) coating and hope for the best.