Hi Christina,
I find myself in much the same situation as you do...I've been seeing a fellow who is with a clinic that does a lot of contract work for the state, people like me with no insurance or private resources. He has moved me to an every 4 week schedule, just when I thought we were getting to the point I was going to start making some progress, but I'm not going to kill myself, so down the list I go! You got it right in your first post...~free~ therapists just can't see people like us long-term, there are too many others who are in crisis. I'm afraid it will always be that way.
As for your options, it sounds like the student is your best option at this point...he's free, and he seems to want to do the sort sort of therapy you feel would be helpful. I imagine that you two can work out your other issues.
Private therapists are kind of a crapshoot...they're expensive, and there's no guarantee that things will work between you. On a student's budget shopping around for a private therapist will be difficult at best. As a general observation, however, I have to say that I have had a couple of therapists that I didn't particularly like that were very helpful. I wasn't expecting too many warm fuzzies, and they were able to illuminate things for me in a way that therapists with whom I had a "warmer" relationship simply were not able to do. In other words, they could say the "hard" things that I needed to hear and not mush them up so much that I didn't get it.
Have you investigated any group therapy or support group options? I have found them to be quite helpful and free or very low cost to boot...something to consider. One of my old pdocs ran a bipolar therapy group with a psychologist weekly for $25...two of the best people in town. Perhaps you could find something similar for depression.
So anyway, there's my $0.02...I hope you find something that works for you so that you can keep getting better. You have so much to offer, never forget that!
DJ