I have finally found my answer! It lies in the physics materials of the tilemap.
First, I went to the Physics Layers menu in the tilemap inspector, added a new element and gave it its own collision layer:

Then I went to the tileset tab at the bottom of the screen, clicked on paint, selected "Physics Layer 1". clicked on my platform tile, and enabled one-way collision:

And voila! With the player script toggling the second bitmask, I can drop through as many platforms as I want while still not falling through my red tiles.