All US major airlines will gladly accept single engine turbine PIC...as long it is in one the following airplanes:

F-16
AV8-B
F-35 (if have this in your logbook you will be hired for sure)

They only allow SE turbine PIC for the sake of the fighter pilots...caravan time alone won't cut it. Your case is unusual...with a little 121 turbojet time they might actually consider you but I'm not sure. Unfortunately, there's only one way to find out.

BTW, anything is better than mesa...trust me.