Man.. I'd go the opposite way. There's no way my fingers could take using 10's or 11's. I'd be trying to adjust the pickups or replacing them... using EQ etc.. and working on getting a good sound from the amp and effects.
If you're fingers can take it and you don't mind the fact that bends and vibrato are going to be hard to do, then go with the strings. It's the cheapest route and worth a shot. All I can say tho is, ouch. jeez... using 11's would be like playing lead on an acoustic.