FWIW -
Went from TPIC at a Willow Run Freight operation to NWA in '01 with 5000TT, 1200 TPIC - so it does, and can happen. I know a bunch of guys who came from the 135/corporate crowd directly to a major.
My .02 - stay where you are and get that TPIC time
PM me if you'd like
Like the name says....
FD