This is an interesting discussion, but this claim struck me as odd:

If something exists, it can be counted (or given a cardinality, if it is infinite).

This seems like an open philosophical question. Clearly you are a finitist of some sort, but as far as I know it hasn't been empirically verified that real numbers don't exist. Certainly continuous functions are widely employed in physics, but whether all of physics can be cast into a finitist framework is an open question last I checked.

So your assertion above doesn't seem firmly justified, as uncountable entities could exist. I have no informed opinion as to whether worlds must be countable or can be uncountable. It certainly seems like they ought to be countable, since the total number of particle configurations in the universe at any given moment in time seems finite, but that's just an uneducated guess.