What I use for stripped allens in general is a very extensive set of driver bits; metric, allen, torx, and straight (like for screws). I find one that just barely will not go in, then I drive it in. The soft metal yields to the new shape and bites while the gentle hammering helps loosen corrosion through vibration. If I can't find a bit to work with I grind a taper on a straight bit so that it will partially enter then I tap it in as above. So far this has worked 99% of the time and when it doesn't, drill the head off or drill the fastener out.
Same (apparently common) problem, relatively easy fix:
I used a #2 screw extractor (specifically a titanium nitride coated SpeedOut part) essentially mounted in a cordless impact driver set to reverse. The screw came out with negligible effort.
BIGWALT nailed it!
I bought the correct tool (my Moen took the torx 1.5) then added a dab of the valve grinding paste ($3 from amazon) to the tip. For the first few counterclockwise turns I used long-nose locking pliars around the torx wrench short end to keep the pressure steady and the tool straight. Sucker came right off.
Can't tell you how long I sweated that one. That little nut turned a 20 minute/$20 DYI into a potential disaster. The valve grinding paste idea was genius!