I keep reading this "ask any old timer pilots"..
I've managed to meet quite a few command pilots for cathay, qantas, dragon air etc.. All say stuff it just get your arse into a jet and try your absolute hardest use us (your connections) and get into it.
They have said on multiple occasions, "forget the smaller GA because that's one thing I wish i didn't bother with for a career as I'd prefer to do that for fun and get in the big ones, been in the industry 25+ years (one 45)
These are guys in their late 50's (most) really nice blokes, on good coin willing to help out on multiple occasions.
I think do what is best for you, try and fight your way into the industry (not literally but get your foot in the door anyway possible) Because whats right for one might not be right for you..