I find men's groups with more structure do help with those problems you described. I wouldn't be so early to dismiss and suggest considering it with an open mind. At least for me and many others I Know, men's groups with a clear order of gather to discuss, and require and ask for consent before giving advice, with that recurring meeting being the main source of socialization; do not have as much of a pecking order nor lame topics. They have more authenticity and connection with the pretense being around connection and acceptance without performance.

If you want regular socializing with 2-3 good friends though, I think the friends made from a men's group would be closer to what you are seeking than from a random hobby-based group.

edit: in re to "even without competition a pecking order gets established" my experience has shown this to be oversimplifying it. The "pecking order" in a mens group is way different from a different group. the pecking order in men's groups with a structur-based leader, is that the leader gets the "alpha" status if there was one and if they are a good leader they aren't there to abuse that privilege. But since they should be providing it professionally (paid service) it isn't mixed with friendship as much. At least the "pecking order" there is oriented around serving you rather than random socialization without that purpose.