Superpilot,
That's kind of a misnomer. Flight instruction is a "real" flying job. If you get paid for it then it is a job. In fact, if you're a good flight instructor, you probably work harder than many higher paid pilots.
To answer your question, I got my first non-instruction flying job at AirNet with about 1700 tt. That seems like a lot of time from your prospective, but it's not that much. I built quality time there. You could certainly expect to be a captain if you applied with about 1450 tt. After training, adding a plane, and IOE, you'd probably have your time.
I think the point is, hold on to the good thing you have. You don't need to jump at a regional. If you really are dead set on an airline job, maybe you should go to a regional. Just know that you will be away from home, probably on reserve (i.e. not flying), and not making more than you make as an instructor.
I am thankful for the job I have now, but I always look for new opportunities. Believe me, I know the desparate feeling of looking down on another day of flight instruction- with no end in sight. However, be picky, you're an aviation proffesional.
If I were you, I'd stick out flight instruction. I'd get 135.243c mins. (these times are a good ballpark for most jobs) and as much multi time as I could (you're multi time is doing well, proportionally). Keep your instrument skills sharp. Get to know pilots of flight departments in your area. Get as much info about QOL, pay, benefits, etc. of the kind of flying that appeals to you. Then, go with that direction. It's just my opinion.