Now, hear me out, I'm not completely bonkers.
My theory is that with 2 Tanks and 8 Shadow Priests this would be possible. With 8 Shadow Priests pulling 15k DPS (easily possible and just about average) that equates to 2800 HPS on the entire raid. Meaning people will be over 10k in just under 4 seconds. Shadow Priests will also be pulling a further 450 HPS on themselves. This would be enough to heal everything including Double Attacks (With a Prot Paladin WoGGing himself in decent gear (Shadow Priests can also roll Renews on the Double Attack tank). During Feud a Diving Hymn rotation can be executed and with a Prot Paladin and Feral you could use Holy Radiance on every Feud, 2 Hymns and a Tranq on 1 Feud, 3 Hymns on a 2nd Feud, 3 Hymns on a 3rd Feud. I think, mathematically it could be done, not sure however.
Also, I'd love to see it attempted with 23 Shadow Priests and 2 Tanks on 25man
Ofcourse, I am talking about normal. Also " Why do it stupidly when you can just kill it normally " It's called having fun and doing things differently, it could also prove to be challenging.
Love to see a bigger guild/bunch of people trying to do this.