My main question though: would I still be plagued by occasional DRM non-starter issues in certain streaming apps if I switched from using Android Grabber to using a HDMI Splitter/capture device instead?
You shouldn't, although i don't use Netflix or such, but i use my setup with a PS5, and some games has DRM sections (usually cut scenes) and those work with the splitter setup.
I can't comment on Hue Sync Box, the only advice i can give you is related to Hyperion (HyperHDR).
So I have a 2019 Nvidia shield, a RPi4 which is connected to an Adalight compatible controller+lightstrip. Initially i was using Android Grabber, but i give up on it for multiple reasons. The main one, it couldn't handle HDR, it eat up CPU processing, but the most annoying is that the service randomly crashed so i had to manually restart it.
So a couple months ago i switched over to a Capture card setup. I bought this: https://www.amazon.de/dp/B08D3…7091401_487024491_TE_item , this has HDMI passthough. Which works, kinda, CEC is not supported. And since i'm pretty used to CEC, i had to by the same splitter as you mentioned. That has a perfect passthough, including CEC.