1. The discovery of the electron reduced the amount of mass attributed to particles and increased the amount of mass associated with the energy of momentum.
2.Each discovery of smaller and smaller particle components in motion reduces the amount of particle mass and increases the mass associated with the energy of motion.
3.If the ultimate result that all particles are ultimately composed of “photons as a standing wave” then there is no particle mass at all but only momentum mass.
4. Einstein’s equation E = M x C^2 predicts that any energy added to a mass will cause that mass to increase.
#4 appears to be the basis of your thinking. Your interpretation is incorrect. What Einstein said is that if you are able to convert mass to energy, THAT EQUATION TELLS YOU HOW MUCH ENERGY YOU WILL GET.
The equation that relates the increase in effective mass to particle velocity is different:
Meff/Mrest = 1/sqrt(1-V^2/C^2) where V is the particle velocity and C is the speed of light.
This equation is very nonlinear in energy vs mass.
Only in the low V/C limit, does it become linear:
Meff/Mrest ~ 1 + (1/2)(V/C)^2
Defining Erest=Mrest C^2 and Eeff= Meff C^2,
Eeff ~ Erest + (1/2)Mrest V^2
which is equivalent to your thinking
Eeff ~ Meff C^2
but only in the limit that V/C goes to zero. However, we can see from the previous equation that even in this limit the rest mass and rest energy does not change. Please in the future base your thinking on the following nonlinear equation:
Eeff = Mrest C^2/sqrt(1 - (V/C)^2)
It is clear from this equation that the rest energy and rest mass are constants independent of the velocity of the mass. That velocity is relative to the observer anyway. So the observer could be moving and the particle not moving; and the equation would be the same; and obviously that would not increase the mass of the particle. That is the whole point of relativity.