I also want to acknowledge that I was being a little flip when I said "find therapist #10"

Don't necessarily give up on your current therapist. I'm sure the suggestion to get your family involved was a good one, but if that is not going to happen, let the therapist know that and see how they want to proceed. If they insist that there "can be no recovery without family participation" then that's when I say go for a new one.

I mention this because with depression our minds often misinterpret things. What your therapist might have meant as a suggestion, you depression may have turned into "well, then there's no HOPE if I can't get my family involved". That's what depression does, it distorts things and finds any loophole I can to exploit negativity and hoplessness.

Make sure you understand the therapist clearly, make sure that HE understands that you have tried, and family participation is a no-go, and then work together with your T on healing and recovery without the family. And then, as I said, if there is still a stumbling block, I'd search for another therapist.