I've chosen floating thumb because I just can't talk my ring finger into staying still when I'm doing quicker runs (like some Iron Maiden lines), but one of the things that helped me the most was learning the part slowly as usual, and then consciously deciding when my thumb was going to move to the A string. I tried to let feel dictate it, but I would find myself hesitating or "being late" to the mute, so I would build it into my learning of the song itself. Now, I don't need to do that as much after a lot of practice.