There are other multi turbine jobs out there in the 135 world you would be able to get. Heard of Ameriflight or other feeder freight operators? If you truly want the PIC time/ATP you can get it if you want it. You may even get that ATP knocked out when you complete your type rating.

Just to help with your restless mind: There are some of those out there that have done the 135 route and got the ATP and PIC yet find the doors aren't opening up because we don't have the highly coveted jet time in a 'glass' airplane.

FWIW i've been to the interview with Cathay and they want PIC in something multi crew and a turboprop at the very least. I wouldn't be too hung up on Cathay though.