I think a lot of it...likelihood of success...has to do with the specific group's dynamics, regardless of interest area. So like with book clubs...some will be good and will welcome new people in, and others will suck, and everything in between. Just because you like reading books doesn't guarantee that any book club will bring what you're looking for. So then you have to check out other groups until you find your "tribe".
I'm no expert at this myself...still haven't found my tribe, if that even exists for me. But...my DH is also something of an introvert (really, more of an ambivert). He does best when he has one or two groups that he really clicks with, doesn't need much one-on-one time with people, but wants to be part of a group. So a couple of years ago, he took up bike riding. His younger brother is big into it, and a buddy at church does a lot of it, too.
He joined the local biking club, and I gotta tell ya, this group rocks. It's a huge group, they divide into smaller groups for biking based on ability level (faster, slower, no-drop, that kind of thing), but everyone from top to bottom with only a few exceptions is very supportive of everyone else. Like, a guy in one of the lower-level groups had a birthday the other day. He's been a long-term member, and a whole bunch of people from all different levels showed up to celebrate his birthday after one of the weekly rides. It's exactly the kind of team atmosphere my DH thrives in.
But it's not because it's a bike group. DH's brother is part of a loose group up in his area, and they're not nearly so close or cohesive or structured. My BIL, although he's way more of an extrovert than my DH, often expresses how much he wishes he had a group like ours in his area.
So I guess my point is...if one group doesn't work, try another. It might not be an issue with you that prevents the relationships from growing. My BIL is a very friendly, outgoing person who is very likable as soon as you meet him. And even he has trouble finding connections when the group is not clicking well.