I'm wondering what other means of physical existence can you devise not based on fundamental interactions.

As I said, anything that wants to pop out into our reality has to do so by changing what was there before, somehow. I'm not saying that supernatural or transcendent phenomena do not exist. I'm just saying that if something wants to manifest in our reality in the slightest, it has to do so through fundamental interactions. I can not see any other means to hold up reality. If consciousness, or the soul, or reencarnation, or ghosts, or angels exist, they have to be emergent phenomena formed by a specific subset of interactions taking place in a particular way within the whole network of interactions that shape reality each time, like anything else that exists.

If some phenomenon seems to break or defy the laws of physics, it is because the interactions that define it let it do so.