We can prove that everything that exist is infinite: if it consists of N elements and no more, there should be some process which limits its size as N and no more. However, such process will be N+1 element.
Or in other words, if universe appeared from non-existence once, infinitely many universes can pop-up from existence independently, as there is nothing which can stop such pop-up process.
However, the list of observer’s states which can appear is finite and is limited by the size of maximum possible causally connected universe. I dissed different ways of counting here.
Interestingly, if she never exists on Tuesday-Heads (and never reappears on Wednesday), the situation starts to look like quantum immortality for Monday-Heads. Their only “continuation” now is Tuesday-Tails.
Quantum immortality analogy also is applicable to the lines where she never appears at all like in 6-sides dice experiment which you described above.