First, the restrictions on your account are because you've been breaking the site guidelines. The way to get those removed is to provide evidence that you've stopped breaking the guidelines and won't break them in the future. That has nothing to do with any of this other stuff—it's not as if being right about bias or demographics (if in fact you are) would make it ok for you to break HN's rules, although people often act as if that non sequitur were true.

Second, it's not obvious how to study this kind of thing quantitatively without making interpretive calls, and whoever controls the interpretive calls completely controls the outcome of the study. In other words, all this would do is reproduce the same cake at a meta level, just with a distorting layer of pseudo-objective icing. The chance that anyone with strong ideological passions is going to run some quantitative analysis about this and come up with anything but the conclusion they already believed, is approximately zero. Has there ever been any study of this sort that did that?

I'm not saying that a good quantitative analysis is impossible, but it would need to rigorously account for this effect (of people reading into the data what they already perceive and believe). How to do that is not obvious, and any 'offer' that comes without a serious plan for it screams bogusness to me. I don't mean to imply that you're intentionally making a bogus offer, just that one would be foolish to take it.

Besides all that, the one empirical analysis you've offered so far ("I watched you single out all of my comments, and then later go back for a second pass to flag the other posters too after you read my profile description") was completely imaginary. That's hardly unique to you—it's just devilishly difficult to perceive these things objectively. The mind simply can't resist its own narratives.