With space and matter density, you plow the very familiar field of our space time universe. Space and density are very useful concepts for our brains and are ones that we really cannot do without. As long as you have space as an axiom, though, you will keep ending up with some version of space time.
However, you can equally well describe all inertia and action as just changes of matter in time without any reference to space and that is the matter time principle. In this case, space becomes a result of action and is not causal. The Lorentz invariance is embedded from the start.
"The Lorentz curve is typically constrained to mass increase with velocity, but if given an added degree of freedom it could equate as density change, what Steve might call 'exchange of matter'."
By Lorentz curve you must mean Lorentz invariance as E = sqrt(m2c4 p2c2), which includes momentum. You want to add a term to get the pilot wave thingy to work...and there is a further energy term in matter time. For objects like stars that undergo serious matter decay over time, i.e. luminosity, but are bound into galaxies, a new term does show up in the virial equation and in this GR expression. It is (dmstar/dt) vstar (rstar-ro), and this interaction shifts angular momentum from inner stars to outer stars in a galaxy, from inner galaxies to outer galaxies in a cluster, from inner clusters to outer clusters in a supercluster, and from inner filaments to outer filaments in a large scale structure.
This interaction makes what we interpret as space, what I call the boson matter wave that is the universe, and so in a sense, you are right with your pilot wave thingy. Each particle in space is a matter wave and there is a complementary matter wave in the boson matter of the universe that is what we think of as space. The spiral density wave in a galaxy is a result of such a matter wave where the star inertial mass is mi = mstar (1 v2star/c2 vstar/c2 (rstar-ro)(d ln mstar/dt))), not only increased by it velocity, but also by its luminosity. This is what causes the galaxy to rotate like a rigid rotor, not dark matter.
If you see where this leads it means that there is an inherent matter decay, mdot, that likewise is the glue binding electrons to protons as charge force as well as binding matter objects to the universe as gravity force. Since the universe as an object of boson matter also decays, the objects that are bound to it appear to move in response to a force in space that we call gravity.
Objects in matter time do not move in space because of changes in momentum, objects exchange matter with other objects including the universe over time and the amplitude and phase of those exchanges is what both our brain and science imagine as motion in space, the giant whiteboard of our mind. So while space along with our number system are both useful and even necessary artifices of our consciousness, the many conundrums of space and of our number system are barriers to understanding the underlying simplicity of our matter time reality.
But each matter wave that undergoes decay and that decay represents a corresponding ripple in the boson matter wave of the universe. They both exist as complements of each other and so neither matter wave is the pilot of the other...they are more like cocaptains.