Ride 20miles a day, (1.5hrs) everyday rain or shine with your current bike! You will kick that hill arse in no time! HTFU. Once your a bad arse with enough leg power to skid while seated then re visit this question.
I moved to Portland with a 26lb Walmart Alum conversion with a 12lb wheelset and a 4lb fork. After riding EVERY day for a Year I felt strong as hell 46x16. I had only moderate time going up hills here. Now I have a 22lb conversion! I mash up hills seated now! Work on the engine first. A lighter bike will only hinder your training!