I don't find Heterodox even the tiniest bit reputable, no. They represent someone's entirely-unsubstantiated opinions and personal feelings, with zero reputable data or research to back them up; and even among opinion-blogs, I'd classify them in the "crazy kook" category. To me, the fact that you consider them reputable for anything severely hurts your case.
I linked Heterodox, which while not peer reviewed is reputable. Do you really think colleges, which have objectively much higher rates of liberals than moderates or conservatives, are going to fund studies on which political party does the most disinvitations? It's an obvious fact that the left is doing way more disinvitations, I really don't see how that can be disputed, even anecdotally.
I don't agree with your assertion that colleges are biased at all, and I completely and unequivocally dispute your implicit assertion that the left is less likely to listen to speakers it disagrees with - consider how many left-wing speakers are invited to conservative Christian institutions, for example. You're just spilling out your gut feelings about the left here, not anything useful or relevant to reality.
I will point out that you are apparently arguing that we should disregard all of academia (because you personally feel it's biased, based on, I guess, your gut feelings) in favor of your favorite blog. Again, this ties into what I said above - your absolute insistence that you have to know everything has manifested itself in extreme anti-intellectualism; you're literally arguing that all science and all academic research is unreliable compared to your gut and the random selection of blogs that give you a warm fuzzy feeling in your gut. I am sorry to be the one to tell you this, but no, your random angry-ranting-conservative blog is not on-par with the entire academic establishment, reputability-wise.
In other words, you admit I'm convincing and you can't substantiate your right-wing smears. Come on, man. You used a vapid talking point you read on a blog somewhere and got called out for it. It's all right to be wrong now and again (and you are very, very wrong here), but you have to at least admit it when it's this obvious. When you're reduced to saying "yeah, well I saw it on a blog somewhere, and I know this goes against all reputable research and all of academia, but they're biased", you've basically ceded every single point. Is this view of the left really, really important to you? Like, is your entire perspective on politics based on "I saw this on a blog somewhere, and it felt right?"
The rest of your words were very flowery, but I couldn't find much substance, so I don't feel compelled to respond to them.
I know you want to feel smart. I know you want to feel like you have some deep secret understanding of politics beyond what the man is willing to tell you. But a vapid buzzword like that mined from some shitty rant on a right-wing blog isn't a constructive way to approach conversations about politics.