If every week is too much, then perhaps every other week?

I have been depressed for many years, and didn't realize it. I have seen three different counselors in the past several years, and for whatever reason, they all devolved into sitting and chatting with an understanding person and not much else.

I am now waiting for an appointment to try a different therapist who uses CBT and other techniques that I think would be useful for me.

You mentioned DBT, which I read is similar to CBT. Since I am 6 weeks from my initial appointment, I have decided to start a CBT workbook on my own. Perhaps you could get some of the benefit of more frequent visits by doing something like I am doing, and report to the counselor whenever you do get to see them.

Keep taking advantage of whatever help you can afford!