But how can I treat each split screen as a multicam and switch camera angles for each split-screen region?
Arrange the splitscreen layout that you want on a new timeline, then convert it into a Compound Clip. Then open your Multicam clip as a Timeline and add the Compound Clip to it. Then it will appear as an available angle in the Multicam switcher.
Edit: in case I've misunderstood you, and you want to be able to change eg the left split screen while keeping the right split screen the same, you should create multiple Multicam clips and stack them on top of each other in the timeline. Then you can select their angles independently.
One consideration is I'm struggling for quality here: some of my camera angles are cropped/zoomed/positioned from one wide 4k camera, others are 1080p
You might be able to improve things with a bit of sharpening. Look for the blur/sharpen section (rain drop and triangle) on the colour page, and start with a value of 0.47.