"would I be able to go to a major without going to a regional first?"
Maybe. It all depends on the situation at the time. I never worked for a regional. UPS tends to hire from a variety of backgrounds, to include regional. Yet, if there is no hiring, it really makes no difference. You can't predict 10 years down the road. If you'd like me to back up 10 years, I could say that you could get hired at a major with 135 or corporate pic jet time. But there are no guarantees in this biz and no way to know the future.
Personally, I think when/if the economy turns around and age 65 works itself out, there will be movement in the career. Sky will say it's not a job worth having. I think it is. It's really up to and your situation.