I keep on feeling like I'm following the argument, but then I keep stumbling across the "supporting moral beliefs with facts" part, and it just seems like it's missing something basic.
You can't ever "prove" moral statements just with facts to begin with, that's the whole point of Hume's Guillotine or the is-ought problem. A moral statement with supporting facts is always, by definition, going to also have moral statements supporting it as well, and it's turtles all the way down; the moral statement is ultimately going to be resting on at least one "moral axiom" aka value aka opinion. So of course focusing on facts isn't going to be wholly convincing.
And personal subjective experience is an appeal to emotion. Those are convincing in the moment, but they're rather ephemeral. Any moral conclusion needs to be recognized for what it is; if the reasoning is valid, it rests upon values that might just be different than yours.
One anecdote... I recently had an extremely disappointing multi-day discussion with an old friend who I discovered attended the insurrection. (Did not enter, but made it to the Capitol steps.) I was at first shocked and dismayed, but then through the bonds of our friendship we were able to empathize with each other's emotional experience, why his community was important to him, etc. We thought afterward that maybe we really would be able to have a respectful exchange of views. But then after that it was just disappointment again - it became clear that he just wasn't going to let go of the belief that it was all staged by Antifa, no matter how much I disproved his various meme jpgs. So at least in that case, that intermediate phase of sharing personal subjective experience only really went so far. (We're not in touch anymore.)