Well, I did it. I was having real problems on Sunday and Monday, but by the time the day actually came today, I was feeling way better. Let me talk about what happened. This might be useful to others who have Kaiser.
It actually went really well. Kaiser sets you up with a separate person on your first visit, not the clinician you'll eventually be seeing for individual therapy. In my case, it was a LCSW (which requires at least a Master's degree in psychology or social work, I believe). He was really nice, and I felt he both knew what he was talking about and was very understanding. That first visit is primarily for evaluation. They look at the initial survey you fill out, and then they talk to you to try to get a feel for why you've come in, what your history is, what your current issues are, etc.
Personally, I'm not very good at being direct when I'm talking about something I'm uncomfortable about. It usually takes me a bit to cut to the chase and spell things out. But once we got rolling, he really seemed to understand a good bit about trans issues and got a good feel for where I stood.
At the end of the first session, they discuss your options. They seem to have a lot of support groups, and he recommended some for me. Primarily the support groups were for some other issues in my life. I might go to one of them. In my case, he also recommended I return for individual therapy. He said they have one person on staff who is very experienced with gender issues, so I asked for that person specifically, and now I'm going to be following up with him.
He told me a little bit about Kaiser and where it stands on the trans issue. From what I gather, it's actually a great option for trans individuals, provided you're in the right place. Orange County seems to have one of the very first full programs out there for trans individuals, including surgery. He even said Kaiser would be willing to cover many of the transition costs. I'm guessing things might be worse in other areas..
I assumed I would be fighting an uphill battle against my insurance provider for help and coverage, but I instead now feel that Kaiser is in my corner. I actually feel a lot better because of that.