Humans, indeed animals in general, inhabit rather complex spaces that include position, phase, velocity and so on across an array of species specific observables. Without motion and our various measurements of it we do not experience. It is an inter-subjective series of conceptual designations that are what we call living in a 3-dimensional world.You don't see how the configuration space of the classical Hamiltonian or the Gibbs distribution is not the physically real space we live in? You don't realize that we observe 3 spatial dimensions and therefore live in 3-space at the length scales of classical Hamiltonian and statistical mechanics? Something must be wrong with your senses and your detectors!
The utter and complete relationality of what is 'real' extends to the ontologies that we establish inter-subjectively. Current physics is an excellent example of seeing 'reality' dissolve under analysis. In fact it makes excellent sense to say there is no physical reality, in the sense that you defined as that which simply exists in the world independent of our sensory observations and experiences of it. There are no quarks, or solitons or clouds or rain or stars in the sky save for our collective conceptual designations of recurring patterns of the arising of the 'real'. It is these designations that constitute the ontologies that are operational among of group of people - some of whom may self identify as scientists.As for defining 'real', that is simply what exists in the world, independent of our sensory observations and experiences of it. Any conceptually consistent physical theory makes some statement about realism. There exists no self-consistent theory that only describes a subjective world of events. Indeed, if you really give time to think about it, it doesn't make philosophical or logical sense to say there is no physical reality.
In the olden days science was an activity striving to achieve a view of that which is from a vantage point outside the 'real'. It is increasingly clear that trying to look behind the veil is not the most effective way of doing science.
That is, science as a group endeavor to establish conceptual designations of patterns of the arising of that-which-is that enable us to get out of harms way and improve our lot, which includes for some of us achieving satisfaction at seeing some patterns and ways of identifying these patterns that have some quality we call aesthetically pleasing.
It is fair to suggest that there is a way in which that-which-is arises, i.e., there is 'reality'; however, it is equally fair to understand that how it arises transcends any ontology in the sense that the complete relationality of that-which-is is without any conceptual bounds.
Schrödinger and Heisenberg had two different ontologies for the same observations that were then extended by Dirac and then Kline-Gordon, Feynman and so on. These ongoing shifts in view are not nailing down that-which-is independent of our view of that-which-is and what observations we can make and want to make for whatever purposes.
It is clear that physical theories are about the observations that we can make and ways in which we talk about them. We can not make all possible observations, and hence we can't talk in a complete sense about that-which-is, i.e., objective physical reality.
I would agree that there are always at least as many ontologies at play as there are people doing physics, if by ontology we mean conceptual frames of reference or equivalently systems of thought about how to talk about the patterns of observations that we are making.