I don't have a lot to add to this (without, as you say, responding in the style of the game perhaps), except to say that I think we're in enthusiastic agreement. Nonetheless, some follow-ups:
- I view mathematical realism/non-realism much in the same way I do fictional realism/non-realism. Which is to say: yes to each, at various times, as necessary or expedient.
- If you're into Quine-Duhem, you're gonna love Feyerabend. He gives the strongest possible version of that claim, and Against Method lays out the argument systematically, drawing on as much historiography as theory. It's an underappreciated book, and one that has completely shaped everything I've done since I read it.
- I'm reading the randomness as a "training wheels" method of getting outside, which we can shed as we come to fully embody the skill. Once we lose the need for "artificial" methods like randomness, we have a more direct access to the Otherwise Than Ourselves, hopefully moving beyond even the limitations imposed by the game (tip of the iceberg, after all) and into the world of the empathetic, the subjectivity of the Other. This absolutely requires some facility with breaking down the Outside-Inside dichotomy, which was always false anyway. (Side note: this gets right at a central point of Against Method, that practice/theory or evidence/theory are not separate, and cannot be. We are always doing both at once, as one gesture.)
I know you're busy these days, but if you end up reading Against Method at some point, I'd love to chat about it! ❤