I'm not a fan of Peterson, but from the bits I've looked into I find the part you highlight most attractive.
I come from a deeply religious (Evangelical) background, and in some ways, perhaps, my situation is 'worse' than yours because I never left because I felt that it was burdensome. On the contrary! I loved much of it and in hindsight the structure and social life it provided me might've been extra-valuable in light of my Asperger's. I just couldn't believe it, and moved to another city, country, etc.
While I'd like to say I figured it out in the interim, I'm still very much working on that. However, I found that at least on the personal level, zen buddhism has filled a significant part of that void, and if you haven't looked into it I can highly recommend it.
I've not looked into the more social aspect of it, though. That's high on my list. I'm bracing myself for a degree of disappointment, because I often don't really like the 'woo-hoo buddhist types' that I run into who are or claim to be buddhists. But I have no real evidence for that.
Nonetheless, despite my ongoing 'search', I feel zen has provided enough that I feel I can be some degree of content without running back to more 'traditional' religion (and I have considered that, up to going back to an evangelical church).
If you're interested in discussing this further, don't hesitate to send me an email.
I personally think there's a very valuable role 'us' ex-evangelicals/ex-religious folk can play in this growing sense of emptiness that I see all around me, and that I see turns people to various 'extreme' movements that all strike me as rather less-than-stellar (alt-right, extreme SJW, rabid marxists/anarchists/whateverists). I'm still often shocked at how many nonreligious folk around me simply do not understand the sense of community that, among other things, a church can provide. It's like talking to someone who has never been in love!
EDIT: Let me add that I don't immediately have anything concretely against Peterson either, and the article kind of confirms my suspicion that he's a bit like C.S. Lewis, which I consider mostly a good thing. I would not want to deny anyone the positive role Peterson could play in their lives, in the same way that Lewis played a very important role in my life. Peterson makes me uncomfortable in a way Lewis usually didn't, but that could be because my point of entry was, well, being deeply religious.