The main novelty in the thermodynamic interpretation is to regard that what is usually called an ensemble mean as in fact being an observable value. Thus quantum mechanics is at the same time a classical and a quantum theory; the natural hidden variables are Wigner-type multi-correlation functions.
For example, the classical hydrodynamic equations are obtained by looking only at field values (and projects the remainder away), and the Boltzmann equation is obtained by looking only at local 2-point correlators (and projects the remainder away). Adding local multi-momentum fields accounting for multparticle collisions adds observables that are more and more difficult to observe, and if all multimomentum fields are present, we have the full gamut of hidden (but in fact not so hidden) variables. Their dynamics is described by quantum field theory; in fact by generalized Wigner transforms of the Wightman n-point functions.
Clearly the field values in hydrodynamics are observable in a classical sense, though not very accurately. On the other hand, in a quantum field theory, where operators are space-time dependent, it is impossible to obtain a true ensemble, as we cannot repeat experiments at the same space-time position. Thus in quantum field theory, ensembles are purely fictitious.
A quantum theory of gravity must account for quantum mechanics of large bodies, such as a star. But the interpretation problems are already apparent for much smaller bodies, such as a glass of water. Each particular glass of water in equilibrium is a single quantum system, but all the observables we customarily ascribe to it according to classical mechanics are true observables of the system, observable in the single instance, without having to postulate ensembles in the statistical sense.
The thermal interpretation extends this to all quantum phenomena. A measurement is simply the recording of field values of some classical apparatus, described as part of the dissipative quantum system consisting of the apparatus and the system of interest, with the environment already projected out. This ensures that measurement values are definite and irreversible. Moreover, traditional analyses of observed quantum measurement processes imply that this interpretation of measurements gives a correct account of the observation of microscopic systems (though the traditional measurement terminology there is very different).
Regarding physics at the Planck scale, I think that spacetime is most likely a classical 4-dimensional manifold. There is a single universe whose states are given by a density matrix, a semidefinite trace class operator on some (most likely nonseparable) Hilbert space. Whatever we observe are classical values of fields (though usually called expectation values or correlation functions) depending on a space-time point and zero or more momenta. In particular, gravity (and hence curvature) is just another field, as this is the way it appears on the observable level. This is both fully local and fully compatible with the thermal interpretation.
Why I prefer this interpretation? Once one has gotten rid of the traditional brain-wash about quantum observables and quantum measurements, one can see that everything corresponds to how we actually observe things - by looking at extended objects and their (in essence hydrodynamic) variables.
How these extended objects respond to the microscopic systems under study cannot be part of the foundations but must be seen as the result of an analysis in terms of quantum statistical mechanics. Thus claiming that we observed a discrete particle with spin when we in fact observed a blob on a screen is something that needs to be explained rather than postulated. (In the thermal interpretation, this is interpreted instead as the observation of a continuous field by means of an apparatus that only allows discrete responses with an intensity-depending rate.) It turns out that the connection becomes stochastic due to the nature of the quantum dynamics rather than due to an intrinsic randomness in quantum mechanics.