EDIT- I see the bike is 7 speed so this isn't applicable to you, but might helpe someone else in a similar situation.

9 speed shimano brifters work with 9 speed MTB rear derraileurs so you can run up to a 36t large cog with the RD-M772 which is an XT model, the older/cheaper M750 model will work with 34t cog, but might not work with a 36 depending on the length of the derraileur hanger on the frame. Both are fairly available on ebay for $40-$60 depending on condition.