I think you should try it. When I started seeing my current T, it was only intended to be a month or two, for consultation on stuff I was struggling with regarding my marriage counselor (and a bit with ex-T). I thought it would be hard to open up to someone new, but I actually found it much easier than with ex-T because I'd been in therapy before. I'd already shared much of my story and embarrassing, shameful things with someone else (really, two people, since also with ex-MC), so it was easier to open up to a new person. Plus, it's like I knew which things were more important to share, since I'd already addressed much of it before (like, I knew what was more resolved vs. what is still a major issue for me).

As I mentioned, I had initially planned to see now-current T for a limited amount of time to address specific issues. So maybe that's something you could do with this T--say, "I want to focus on getting help with x and y." Or if it's that you want general support, but don't want to go into your whole life story, I think that's another way to go.

Definitely worth a shot though.