I did attend one "Jews by Choice" meeting, but I think my experience will discourage you. I saw a note about the meeting in the newsletter of the shul that my sponsoring rabbi leads, but it was organized by an individual and not a shul-sponsored event. At the time, I was no longer an official member of the shul because less than a year before that my "tiny lay-led minyan" had, after five years of being a "satellite minyan" of that shul, lost the lease to the basement room of the former host shul building (which was sold and became an Assyrian Community Center which was gracious about allowing a 5 year lease after that sale). The JBC meeting was organized by the mother of a classmate of my daughter (whom I had no idea was a JBC) and it was at her house just a few blocks from my home. So even though it snowed that night, I just walked on over.
The other six attendees were all older women who had converted when they married their Jewish husbands 30+ years before. One of those husbands came to the meeting too. Then there was me, a bit "younger" than most of the women even though I was in my late 40's, and I had not converted until many years after marrying my Jewish husband. My sponsoring rabbi attended the meeting as well.
The women shared some stories of having been treated rudely because they were converts which rather horrified my dear sensitive rabbi who was relieved to find that none of the incidents had happened at his shul. The woman who organized the meeting said she was wondering if there might be some way in which a JBC group might be helpful to new or prospective converts. As far as I know, there were no follow-up meetings.
I suspect that if you tried to get a JBC group going, you might also find that a majority of the attendees would be women who converted before marrying Jewish men. I hear that most conversion classes are filled with such women. (I didn't take any such group classes, so I didn't personally see this.)
In my minyan, there are 5 female converts (including me) and 3 male converts. I think only one or two of the women converted just before marrying Jewish spouses. the rest either converted well before meeting their spouse, or some years after being married to a Jew. (One man's wife converted to Judaism with their first son who was a baby, before he did some years later.) But a majority of these JBC converted 30+ years ago, and it is really not a very major aspect of their Jewish identity at this point. Three of them were on a panel to discuss their conversion during Shavuot about 6-8 years ago, but I think they were asked to do so by our host shul and they were simply gracious in agreeing to do it. Interestingly, I have discovered recently that a couple of the JBB members of my minyan had a JBC parent which I only found out when the parents' life stories were recounted after their deaths.
Although I technically officially converted only a few years ago, I have been involved in Jewish communities for over 25 years now. So in some ways, I think I am more like the other long-time JBC I know. I am comfortable participating in other Jewish groups and organizations and am not interested in a JBC group despite being in the Chicago area.
I hope I haven't completely discouraged you. I'm curious to hear how it goes though. Good luck, MIke.