Instead, I take the position that you can never conclude anything from your own existence except that you exist. That is, I eliminate all hypotheses that don’t predict my existence, and leave it at that, in accordance with SHA.

This sounds a lot like full non-indexical conditioning (FNC). The standard problem with FNC is that it seems to make science impossible. For, many actual theories predict "big universes", in which every subjective experience is almost certainly experienced by some observer somewhere, even if that observer is just a Boltzmann brain.

Prior to all observation, it seems that you should be indifferent among all these theories, or at least among many of them. But then, on FNC, no empirical observation can give weight to one of these theories over the others, because they all equally predict the bare existence of an observer who saw whatever observation you saw. Thus, the entire practice of empirical science fails to affect your beliefs about these theories at all.