As i mentioned in Fridays blog, having poor thoracic spinal mobility is going to make things difficult, not only for your front squat, but for any movement where flexion through the shoulder is required (front rack position and overhead work).
One of the techniques I used in last weeks mobility class was the double lacrosse ball and bumper plate drill. This is great for clearing up the thoracic.
This sort of work can be done before a class, so if you get in early, grab some equipment and use the upstairs area to role things out. Ideally though, soft tissue work like this should be done away from your training window. i.e of a night when watching tv or during the day (cos you all have time for that, right?)
Spend some time focuses on this area for a week or two and notice how a lot of your shoulder work gets much much easier.