I've watched a ton of JP and yes, he pretty much does say that all modern problems are the fault of feminists and "social justice warriors." But let's not get fixated on Peterson and go on to more interesting topics.
I'm sorry that you didn't find anything good on the Good Men Project. They have spread out quite a bit lately, but one of their top (and best) writers here on Medium is Mark Greene, who I think has a lot of smart and insightful things to say that are specifically about men and masculinity. Check him out.
I personally love men who are confident (but not cocky) meaning that they know who they are and that they own that. But I also want a man who is kind, considerate, and wants to interact with me as a full partner and fellow human being, not some sort of side-kick or accessory. And, truth be told that takes confidence because a guy who wants someone he can dominate isn't confident enough to handle an equal. But I digress... All humans are a combination of Yin and Yang traits so it wouldn't be fair to only talk about the Yang (masculine) traits that I like in a man. In fact, that is one of the main issues with masculinity as it is currently constructed - there is almost no allowance for any Yin traits (as those are seen as "girly" and therefore less than). Both Einstein and Tesla were big proponents of both cognition and intuition. I admire a man like that.
Mostly, I admire a man who isn't afraid to go his own way and to be who he really is despite who he has been told he should be. That ranges from guys like Alice Cooper to guys like Harry Styles - and a whole lot in between. It speaks to not being a slave to other people's expectations - perhaps because individuality is a strong Yang trait. But although agency and sense of purpose are great, in my mind they need to be balanced with emotional intelligence and empathy.
My primary partner is a lawyer, my secondary partner is a cop. They both have a lot of traditional masculine traits, but balanced with a gentler side. Both know how to be friends with women, because they don't only look on them as sexual possibilities. They know who they are and what is important to them. They aren't afraid to show a softer side when it's appropriate. Hot!!!
The APA notes that 40 years of research shows that "traditional masculinity is psychologically harmful and that socializing boys to suppress their emotions causes damage that echoes both inwardly and outwardly." As with the research I already cited to you, that seems rather indisputably true - not as a way to demonize men but as a way to help them. If you culturally aren't allowed to be a full and complete human being, how can that be anything but harmful and destructive? And if you have to always be in control, always have to be stoic and suppressing any difficult emotions other than anger, if you feel you cannot turn to anyone else then that is a problem - because it's not natural. And those are core values of "traditional" masculinity. Which is why it's so harmful and toxic. Again "rotten fruit" not fruit itself.
Several years ago Canadian female lawyers complained about what they viewed as the unnecessarily brutally competitive nature of most major law firms. The same holds true in the US. Women weren't even allowed into big firms until the late 1970s and then it was quite sparingly. So, most firms have a quite long standing male-dominated atmosphere where partners are quite cut-throat and ultra-competitive with each other - resulting in not just an unpleasant environment for women but one that drives law to be the profession that most leads many men to substance abuse, depression, and suicide. But, when Peterson was made aware of this, his opinion was essentially that men should be able to run their law firms in the way that they see fit (even if it is killing everyone). That's what I mean when I say that he glorifies and defends the worst aspects of "traditional" masculinity. It doesn't matter that it's killing everyone, let's all pretend we are lobsters - even though humans haven't shared a common ancestor with them for 700 million years. He alternately defends patriarchy and pretends it doesn't even exist. It's pretty silly.... if it weren't so destructive. So, I said we wouldn't talk about Peterson, but it's pretty hard to avoid him in this.
I write often about the social system of patriarchy and you aren't wrong that it is a whole other subject unto itself, but in essence, it is a dominance-based social hierarchy predicated on traditional power that is maintained through coercion and the threat of violence - something that as far as I can tell Peterson is all in favor of because he wrongly assumes that it is somehow about merit and not inherent social stratification.