Additionally, it's interesting to note that I treat the idea (that existence has no referent) as a hypothesis, and it's a hypothesis which I believe I can collect evidence for and against:

The book "theory of nothing" by Russel Standish contains a derivation of the Schrodinger equation from axioms which are supposed to be purely about an ideal observer and the process of observation. If this argument were convincing, I would take it as strong evidence for the hypothesis: if we can derive the (otherwise strange and surprising) workings of quantum mechanics from the assumption that we're an ideal observer sitting inside of Tegmark IV, that's decent evidence for Tegmark IV.

For better or worse, the argument isn't so convincing: my main objection is that it slips complex numbers in as an assumption, rather than deriving them from the assumptions. So, the complex-valued wave function is not explained.

There is a derivation of quantum logic from the logic of self-reference, and I consider this to be very weak evidence for the hypothesis.

Bruno Marchal does work along these lines, and discusses a world-view with some similarities to what Coscott proposes.