Denise, perhaps I got the idea from you. I know I got it from someone on Susan's. Whoever it was, that is exactly the approach I used for the two neighbourhood groups I came out to in person. In both cases, I made the announcement in a regular meeting of the group.
I said exactly what you suggest: that G.D. is the diagnosis used for people who are transgender, and that I have been diagnosed with it. It made the point that it was a medical condition, and that it was diagnosed by professionals, and was not a choice. And I went on to say that the cure is to transition to the proper gender.
In both cases, I got a few surprised looks, but no negative reactions at all. I got expressions of support and acceptance. One lady, who has had some difficult LGBT issues in her family got teary-eyed and was effusive in her support.
For a couple of other groups I came out to, I did a mass email to the group mailing list. Both groups consisted of intelligent, informed people, so I had fairly high confidence that it would go well. My email read, in part:
Quote. I wanted to give you a heads-up that I am changing my name. My new name will be Kathy. Okay, obviously there is more changing than just my name. I am transitioning to live as the woman I was meant to be. This is not a hasty or sudden decision. It has been on my mind for the last 62 years.
In both cases, I had a huge number of positive responses, and none negative. I feel loved and supported in both groups.
So, yes, I can vouch for your approach.