If you're not set on Roku/Fire Stick as clients and would be willing to use (for example) Android phones / laptops / Raspberry Pis you could consider just makin

If you're not set on Roku/Fire Stick as clients and would be willing to use (for example) Android phones / laptops / Raspberry Pis you could consider just making a VLC playlist and sharing your screen via Discord. This would allow everyone to join the server with an invite, and join the stream with a click. Good max video quality, and handles low-bw clients well too. If you really need scene selection and stuff, then you could use OBS + (VirtualCam + VoiceMeeter) as your mixer and feed that into Discord.