you're basically restating formalism

Not quite: what I have here is game formalism with the additional claim that the games are 'real' in a Platonic sense (and nothing else is).

you can have formal systems that talk about formal systems

But you cannot prove, formally, that formal system A talks about formal system B, without appealing to another formal system C (and then how do you know that C talks about A?). I already made this point in the OP.

if you want your system to have any utility you have to assert the consistency of the systems you're using

Yes, but you only have to make that assertion as a condition of the application; in order to claim that two pebbles plus two pebbles makes four pebbles I have to assert that PA applies to pebbles, which assertion involves asserting that PA is consistent - but if it turns out that PA is inconsistent, that only refutes the assertion that PA applies to pebbles; it does not 'refute' PA, since PA makes no claims of consistency (indeed, PA does not have a notion of "truth", so even Q=PA+"Q is consistent" makes no claims of consistency). Thus, while paradoxes may conceivably destroy the utility of mathematics, they still could not destroy mathematics itself.

the set of all formal system?

Good point, that should have been 'class'. Fixed.