What you have is a common problem but a pain none the less. The best way to handle this is to use a hand drill and about a 3/16" drill bit. Just drill into the orginal hex hole that's stripped. Drill deep enough and the head will come right off the threaded portion. Remove the module and turn out what's left with a pair of pliers. No need to drill into it from "the back" as it is hard to get centered and you take the chance of messing up the threads in to cam.
When installing a new screw, whether carbon steel or stainless, put some bowstring wax under the head (between the head and the module) and on the threads, This should help keep the screw from freezing to the aluminum module. You must do this with stainless as it galls to aluminum even worse than carbon steel.