Matt Benesi said:
Mass contributes to the total stress energy
And the number of particles doesn't, yes.
Matt Benesi said:
someone still had to confirm experimentally that mass <sic> stress energy in a volume of spacetime instead of the number of particles in a volume of spacetime is what causes the deformation of the volume of spacetime
Every experiment that confirms the Einstein Field Equation confirms that. There is no "number of particles" term in the EFE. There is only the stress-energy.
I'm also not sure why you are focusing on "number of particles" here, since that is by no means the only property that objects have other than stress-energy.
Matt Benesi said:
I'm thinking that people worked backwards from detected accelerations (spacetime geometry) towards various astronomical bodies to determine what the mass (stress energy) of the Sun, Earth, Mercury, etc. are...
Spacetime geometry is more than just detected accelerations. It includes all effects of gravity. The most direct manifestation of spacetime curvature is actually tidal gravity, not "acceleration due to gravity".
As far as how the masses of astronomical bodies are determined, the main method is Kepler's Third Law: you observe the orbital parameters of objects orbiting the body whose mass you want to determine, and calculate its mass from those. To determine the mass of the Sun, for example, you measure the orbital parameters of all the planets and apply Kepler's Third Law. The fact that you get the same answer for the Sun's mass from all the planets is strong confirmation that you have gotten the right answer.
If you wanted to test a theory that said that something besides the mass (or more generally stress-energy) of the Sun was what determined the orbital parameters of the planets, you would first have to develop such a theory, and no one ever has. In the absence of such a theory, I don't see how you could test the question experimentally.
Matt Benesi said:
You could also work backwards from detected acceleration (spacetime geometry) to determine the number of particles in them, assuming the number of particles is what determines warping of spacetime instead of mass.
Really? Then please explain your theory that shows how you would do this. And the theory can't simply be "well, we know the mass of each individual particle inside the Sun, so we can calculate the number of particles from its mass". You have to come up with a theory that doesn't use the concept of "mass" at all--that gives a way to determine "number of particles" from orbital parameters of test bodies without ever using the concept of mass. (And since gravity is a mutual interaction, you would also have to have a way of determining the number of particles in the test bodies--each of the planets--without using the concept of mass.)
To put it another way: your experiment in post #3 assumes that the number of particles in a 100 kg sphere of Al is different from the number of particles in a 100 kg sphere of Be. But how do you deduce that? By knowing the masses of the Al and Be atoms. But if you are trying to argue that gravity is determined by number of particles rather than mass, you have to have some way of determining the number of particles that doesn't depend on knowing the mass of anything. Otherwise "number of particles" isn't really an independent concept.