It is probably too late for this now,
since you already have the body and sleeves combined, but you don't have to bind off the stitches at the underarms. You can just slip stitches onto waste yarn as stitch holders, and when the knitting is done Kitchner stitch the underarms together for a totally seamless sweater, and less bulk at the underarm.
EZ (Elizabeth Zimmerman) recommends 8% of the total of the body stitches be held for the underarm and it works really well. If you have access to any of her knitting books, she has directions for many sweaters like this: body and arms knit in the round, joined at the underarms, then knitted as one piece up to the neck. This is my favorite way to do sweaters now.
(Can you tell I HATE seaming.!)