My line of thought has been similar: If all mass/energy curves space time, then by extension all particles curve space time in proportion to their mass. You can't have only planets and stars curving the fabric of spacetime, it has to be the individual particles that make them up, because duh: if you split a planet in two, each half will keep half the mass and hence half the curvature.[1] You can repeat this all the way down to atoms, nucleons, and electrons. Probably photons, quarks, and neutrinos too.
But that's not how anything works in field theory, QED, etc... they just assume that there's a locally flat background with some "stuff on top" that doesn't distort the background at all. Like a function above the number line.
The key insight is that whatever makes particle curve spacetime must be some inherent, fundamental aspect of their nature. Not an extra "m" attribute that can be anything. That's why rest masses of all particles are consistent, their mass -- their curvature in spacetime -- is the very essence of their nature.
My current best hunch is that particles are like knots or tangles in the fabric of spacetime, inherently curving it. All information is encoded as curvature, and curvature is the only thing that truly exists. In this model, black holes are regions of maximum curvature, vaguely like a ball of yarn. If you want to add one extra "strand" going into the ball of yarn, its cross-section has to be added to the surface area of the black hole, which is why black hole area is proportional to its matter content, not its volume.
1] Not quite though! There is the gravitational binding energy. You have to put energy into a planet to split it up into separate particles, and conversely, planets release energy by the mere act of their forming. Jupiter releases more energy from its interior due to gravitational contraction that it receives from the Sun. In effect, particles are heavier separately than together.