I finally did phase 1 of putting proper entertainment in front of the exercise machines:
1. Install https://www.gnu.org/software/gmediaserver/ on my PC and wrap a shell alias around `gmediaserver -p <PORT> --profile=ps3 <FOLDER>` on my PC.
2. `ufw allow <PORT>` on my PC
3. `Settings → Services → UPnP → Allow control of Kodi via UPnP` on my https://openelec.tv/ box.
4. Install these two packages onto an old phone for a remote:
https://f-droid.org/en/packages/de.yaacc/
https://f-droid.org/en/packages/org.xbmc.kore/
Further ideas for when I'm feeling like working on it again:
1. Write a custom web remote for my existing Audacious Media Player setup and install https://github.com/masmu/pulseaudio-dlna
(audman exists, but appears to intentionally make design decisions I don't like.)
2. Write a Firefox extension and helper daemon to expose open YouTube tabs to DNLA for on-the-fly youtube-dl-ing and playback.
3. Combine all three prior options into a really polished web remote to supplant my use of Yaacc.