You need a citation or preferebly a Hawker type rating to land a job with your level of experience. What you are going to need soon is Jet time to stay competitive with the young guys at the regionals.
For a Global or G-V position, they want some serious experience, to include int'l experience and most places require anywhere from 300-500 hours on type for an F/O position. I've been told over and over, a type rating without actual time in the airplane is not worth much. If you get the type, and you go three to four years without actually flying the thing, then it becomes almost useless. Unless you know some company VIP, or the chief pilot is your uncle, a G-V type is going to sit on your dresser doing nothing. Get something you can use.
(ps- there are many Hawker jobs outhere)