Having lived in both the ME and SF, and having flown both corporate and airline, my suggestion would be to stay where you are and apply to a US major. Particularly Delta or United. Both airlines consider corporate pilots in an attempt to produce a diversified new-hire cadre (diversified in the industrial sense of the word).
I don't know how close your company expects you to be to the airport but consider moving as far east as is possible, like maybe the Delta or Tracy area, and using that housing savings to aggressively pay down your debt. But I sympathize with your plight, living in the Bay Area is tough, living in SF even harder. $120,000 just doesn't cut it in such a city. Sure it's a nice place but it's prohibitively expensive to live in unless you're making north of $400,000/ yr. I'm surprised your company can get away with paying $120K for a pilot in SFO.
Do yourself a favor and avoid living in SF city at all costs, save your money/ pay down debt. Been there, done that in SF, for 10 years. It's an over-rated proposition. After you visit all the main attractions twice, all that's left is the bar scene, which is pretty hideous in SF anyway. If you need city life, just take the BART in and get it out of your system. Big cities are for college grads and or career-minded people whose jobs are based in a downtown area. No reason for a pilot to waste money living in such a place.
Of course that's just my $.02 but since we stay in enough big cities for work layovers, I feel I get plenty of the big life that cities are all about. When I get home I like to have space and not deal with traffic/ stress/ noise/ pollution/ cost that is all associated with big cities.
Worse case scenario with the above strategy, you'll pay down your debt. Best case you'll get hired with a major, still pay down your debt, and get to fly big equipment. But I agree with that other poster who said there's no difference between big and small jets. After the initial 90-day honeymoon, it's an airplane. It's all about schedule/ lifestyle after that.