acutrainer: I've also had to deal with serious pain in my minor rhomboid (which could could be confused with the trapezius). I also have a desk job.
The source of my pain was my actually the posture I used sitting at my desk. I did four things: raised my computer monitor 6 inches, focused on holding my head more upright (my bifocals drew my head forward), started doing push ups to stretch the muscle, and did stretches that mimic push up movements.
After six months of discomfort, the pain was clear in 2 weeks.
Just a thought...it may not be the bike and may be something else needing adjustment...
If you don't grow where you're planted, you'll never BLOOM - Will Rogers