More useful than a GPS route, if you're looking for the best way through the glacier, would just be to take off from Camp Muir a little after the RMI parade, following their headlamps. Their groups start out from Muir every (safe) day sometime between midnight and 2 a.m., and they aren't as slow as i'd expect most big guided groups would be. Playing "follow-the-leader" might not be the most challenging way to climb Rainier, but i think it's a better option for getting through the crevasse fields than following a GPS. If you can't navigate it by sight, the weather's gotta be no good for being up there at all.
An obvious good way to use a GPS would be to record your track on the way from Paradise to Camp Muir, in case of a whiteout on your way back to your car. I think it's not uncommon for people wander off route and even sometimes die, even that close to the lodge.