Yes, the simulations split, but those splits tend to either give the identical in-simulation result, or in rare cases to break the simulation altogether. That is, one necessary precondition for my idea is that the "felt measure" of being in a million identical copies of a simulation is identical to that of being in one; and that this is not true for non-identical copies with even apparently-trivial differences.

A quantum computer, or a hybrid of a conventional computer with a quantum source of entropy (random number generator), would be splitting in a true sense. However, the number of quantum bits which were effectively splitting the sim without breaking it, and thereby were multiplying the measure of the sim, would still be vastly smaller than the number of quantum bits on which "reality" depends, and which are thereby constantly multiplying the measure of "reality".

I also give credit to the Tegmark Level IV, computable/countable, multiverse. In that sense, there are certainly an uncountable number of "seeds" for any given isomorphic class of universes, including our own level-III multiverse. Some of these may include an additional level of "simulators" which are "outside" our level-III multiverse; even possibly some "intelligent" simulators who have deliberately built the simulation in some sense. However, those "two-level" (or more) seeds are, in all probability, much rarer than seeds which simply code the fundamental laws of our own, "simple", level-III multiverse. And when I say much rarer, I mean that, if they even exist, the atoms of our visible universe would probably not suffice to express how much rarer in conventional notation.