There's a difference between "gym fit" and "mountain fit" as you'll discover on Rainier. Upper body strength isn't much help on glacier climbs and too much bulk may be counterproductive. I made a similar error before my first ever climb (also Rainier). Since then I haven't lifted weights at all and feel much faster and efficient at altitude.
The muscles that should bear the bulk of your pack aren't upper body but rather in the hips, mainly the flexors but also the abductors as the weight increases. The way to train these is by hiking with a heavy pack or doing a lot of running particularly on hills. http://www.sierratradingpost.com/lp2/backpack-guide/
Also, going guided you'll be expected to carry group gear as well. On my guided Emmons climb my pack was 55 pounds. When I went back a month later unguided it was only 48 lbs. If you're struggling with 40 it's gonna be a miserable climb.