I am in kind of the same boat that you are in except that I am not yet typed in the Westwind. I will be in a month, although.
Since you are typed in the Hawker and Lear, and are getting valuable jet PIC time, I would not leave. And why would you? You are going to sit in the right seat at any regional for 3 - 6 years depending on the airline.
Now I know that being on call 24/7 sucks, God knows I've done it, but it will pay off in the end.
Good Luck