Replacement Shader with Per-Object Instance/MaterialPropertyBlock Values?

I know the traditional way to do effects like an outline is to first render the scene with a replacement shader, and then read that custom buffer and use that information to draw the final effect in a fullscreen pass to the camera.

For an effect I'm working on, I'm trying to draw surfaces to a custom buffer where each object writes a different color to the buffer based on some per-object material property (e.g. this object draws purple, that object draws red, etc.). Is there a way for the replacement shader to use a per-object instance property or MaterialBlock for each object, in a single pass?

This is using HDRP, for reference, where so far it looks like I can only override materials rather than shaders in a custom pass. Unless I'm missing something.