So, there are other quarks than are contained in the set of all quarks.

You've collapsed the distinction between two possible worlds. You started out by saying, consider a universe containing infinitely many quarks. Then you say, consider a universe which has all the quarks from the first universe, plus a finite number of extra quarks. The set of all quarks in the second scenario indeed contains quarks that aren't in the set of all quarks in the first scenario, but that's not a contradiction.

It's like saying: Consider the possible world where Dick Cheney ended up as president for the last two years of Bush's second term. Then that would mean that there was a president who wasn't an element of the set of all presidents.