Sometime in my past experience, I borrowed a plumber's tool from a friend that used a flexible belt to wrap around faucets, etc, which had no wrench fittings on them. It worked like an oil filter wrench; wrap the belt around the item to be loosened, bring it back into the handle and apply leverage.
Your description of the problem makes it sound as if this might work, it you can locate one. Sorry, but I just don't know the technical name for it. Maybe a plumber friend can help.