Not a direct answer to your question but when I lived close enough to commute i used a rear rack and panniers. Found for me I showed to work less sweaty and the rear rack setup acted as a rear fender saving me from the occasional shit streak.
Closer to a direct answer have you looked at using a messenger type satchel vs back pack?
Good luck I wish I lived close enough or had the time to commute.
No Guts No Glory, No Brains Same Story