Perfect Cast app handles Casting .ts streams nicely too.

Or use VLC to play m3u8 and cast to TV

Anyway to do this from iOS without jailbreaking?

This has to be frustrating to use. You should really just save yourself the hassle and swap the chromecast for a fire stick. Even a used 1st gen stick for $10-20 or whatever they're worth would be so much nicer to use...

Sounds like a lot of work for IPTV on TV. I use Pi 3 for IPTV and combination of Chromecast / Plex / NAS for playing music.

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GSE IPTV supports Chromecast by default, been using for awhile. Support Xtreme code and playlists.