Most organisations seem to be happy with something equivalent to a JAA class 2 for a flying job FTE; you are / will be better qualified than I was when I got my first FTEing job - it sounds as others have suggested that the big issue is that first "in".
The FAA licence should carry a lot of weight as showing you know about aircraft operations, and I'd hope that any sensible recruiter would recognise that that, plus the degree, are a pretty good entry qualification set.
G