Hey There,
This may fit with your people, may not. But this is us;
Just thinking outloud, we have a core team which raids Weds & Sundays to now focus on Mythic progression.
You say some of your people don’t care for that, fine. We run a social / alt raids on Fridays every week for our more social members so that they can see the content? Could be of interest?
Were also pretty busy outside raid days with M+ 
Eitherway, good luck in your search!
Cheers