When my wife was an intern (she's now a researcher and doesn't practice psychotherapy, except as a volunteer at a rape crisis center), her supervisor told her that almost all interns become better with experience. He also told her that some interns are better on their first day than experienced therapists are on their last, and that in many ways the quality of the therapy is determined by the fit between therapist and client.

So I would encourage you to give the intern thing a shot, you might find a good fit and someone who works well for you. In our community, the psych clinic (where grad students and interns work), they always have a waiting list because they have such a good reputation for providing quality services. I doubt that you will have luck with calling experienced therapists and asking for free services. I know quite a few T's, and they either volunteer at a free clinic/organization or offer reduced fees to clients they already know. They are not usually waiting around for people to call who want their services for free. Sliding scale is a greater possibility. Good luck.