Heavier strings will definitely solve the problem. Also, I think they sound better, and they definitely retain their tone longer. Although, if you're using 12s, you're almost to the point where the next step is barbed wire... I use 13s, and I do a lot of string bending. When I get on an electric these days, my vibrato is killer, because the strings and scale make it like a hot knife through butter.

I was quite surprised and pleased with the quality of Long & McQuade's branded strings. I'm not sure who makes them, but when it only runs $4 and change for a set of 13s, I'm a happy camper!