As was suggested, you could take advantage of gojet (or mesa) by working there for six months...that will be enough experience to get a job at most other regionals, and won't really help gojet. I wouldn't hold that against you. I'm not sure if they have a training contract though.

You might still be able to get a job at a good major, especially if you have connections. This is mainly because the major airline pilot groups are often unfamiliar with the current regional situation and TSA/gojet. You might be able to slip in under the radar so to speak. However...nobody is going to forget gojet, and as time passes more of the current generation of regional pilots will be moving on the the majors. You certainly would not want ME to have anything to do with the hiring process at any airline you apply to...