Your intuition is really very good...however, your math could use some improvement...
"Yet on that premise alone, wouldn't the easiest model be one where they function as opposite sides of a cycle, sort of like convection, in which energy is radiating outward, while mass is coalescing inward, with myriad complex interactions, such as mass absorbing energy, being propelled by it, resulting in spirals, jets, spheres, polarization, lensing, etc."
In essence, you have described that natural give and take, the yin and yang of matter time. That is exactly why I explore the consequences of matter-energy equivalence and Lorentz invariance with just matter and time dimensions. By the way, this math is strictly forbidden by the orthodoxy of space time, but matter time seems to work much better than space time and yet matter time is consistent with even more observations. Space time resists the idea that there is a structural change to matter because of velocity, but in a decaying universe like matter time, a structural change in matter is what drives all force.
Restating what you said in terms of matter time, objects exchange matter (i.e. energy) with other objects, radiating energy inward as bonds. Objects that bond with other objects do so by exchanging matter (i.e. energy) with the universe, radiating outward. Every bond of matter has a complementary photon of light running around the universe, which is the energy that bond.
Yet, to have the matter-energy equivalence we also have Lorentz invariance. The game of catch, you see, is not between matter and space, the game of catch is between matter and time. Since space is time, you can see why what you have intuited actually does make some sense, at least in matter time.
Again restating what you said in terms of matter time, an object gains matter over action time, radiating inward. An object correspondingly loses matter over proper time, radiating outward and these two times scales are related by Lorentz invariance.