Just a minor point:
“when you have the statement refer to itself, you get a paradox” is not necessarily true. For example, the statement “this statement has five words” is self-referential and true. No paradox. Even a self-referential statement that includes its own truth value can be non-paradoxical: “This statement is true and has two words” is merely false.
By the way, this leads me to consider Prior’s resolution as somewhat problematic:
“This statement is true and has eight words” “This statement has eight words”
The first statement is true and the second false, hence they cannot be equivalent. Nevertheless, adding “This statement is true and ” to any statement should not change the statement’s truth value if we accept that every statement implicitly states its own truth.
Though the number of possible minds is vast, I think the likelihood of two minds sharing an intuitive concept of number is high, because minds (or perhaps I should say consciousnesses) process information sequentially. Perhaps it is akin to the shared perception of rhythm, which is not limited to human minds. I suppose you have already seen it, but this video is amazing: the dancing cockattoo.