I don't wish to be uncompassionate.
But I must respectfully note, I think if you're asking for help to circumvent a punishment by GitHub, one needs to know what the nature of the "controversy" was. There are certainly some 'controversial' viewpoints that are vile enough that I'd rather not help someone who had their views.
I respect that you're in a sticky wicket. But this seems no different from pre-Internet times when one might lose their job from insulting a close vendor or client your employer works with. Imagine you were in a bar in a one-company town talking about a sexual conquest, only to turn around and see your employer, who reveals your conquest was a 20-something child of theirs. Your choice at that point is pretty much to move.
You failed to have the self-awareness that you were in a venue that could affect your livelihood and made a mistake so significant that it can't be retracted or made up. That has happened both off the Internet and on it since time immemorial.
The question you are asking now is not how to handle the situation, but how to continue the behavior of disguising yourself to circumvent the punishment. I think that (a) is a question that shows you are not owning up to your behavior (which itself is problematic); and (b) is the wrong strategy to take in this situation, because any circumvention or working outside the GitHub system is _conceivably_ fragile and could collapse at any point, leaving you with the same problem once more.
My own suggestion - and I make this with reluctance not knowing whether the 'controversy' is something vile - would be to do two things. Both would be extremely hard.
First, I would approach your HR contact, apologize for your conduct with the most remorse you can demonstrate, and see if their person/contact (sales, support, whatever) at GitHub can help you in this situation. Assuming they want to keep you, they can even say to GitHub, "Look, we want to keep this person employed, what can you do for us? Can you provide an ability to commit code without commenting ability?" Etc.
Second, pursuing that guidance separately, I would see if anyone here, or any personal or professional contact of yours (cf. LinkedIn, etc.), has any contact at GitHub, or any friend-of-a-friend at GitHub, etc., so that you can speak with someone personally.
Certainly the repeated attempts (and deletions) at circumvention likely are not doing anything but racking up points on the 'don't let this guy back in' meter, whether that's automated or not.
Lest you think I am unsympathetic, I once made a decision that might've potentially locked me out of a great deal of future employment. I truly believe what made the difference in that situation was that I owned up to my error and looked the wronged parties in the eye and apologized directly. I explained the human factors leading me to make the wrong decision, while explicitly saying it didn't excuse the mistake. Humility is rare enough in today's world that it can oft make a difference.
I wish you luck in your resolution of this issue.