Sorry, I don't know what dependencies are required for libmux_ts to be built. As far as I can see in the vlc sources in file "modules/MODULES_LIST" present at least
* ts: MPEG-TS demuxer
* mux_ts: MPEG transport stream muxer
Unfortunately, I'm not sure that this is all that is needed. Maybe need all mpeg and ts options to work. You can just try enable ts+mux_ts and do test build. Guess mux/demux is simple and not will entail a lot of “heavy” dependencies like graphic ones. Most likely it's just simple code inside vlc tree without many new big dependences.
As another option you can do vlc3-full extension with all monules enabled, huh
Multicast streaming at TC would be interesting, but if it doesn't work out, well... I'll just use a heavier distribution.
Now I’ll try ffmpeg for streaming, but it doesn’t work yet. Studying the manuals and experimenting.