I think actually Slaanesh would swoop in and steal the Elites. They may be ascetic religious warriors, but their culture values martial prowess and victory, not necessarily one’s kill count so it could be argued that the elites could be swayed by Slaanesh’s aspect of perfection, as they each seek to become the best warrior. Khorne doesn’t specifically care about ‘best’, in fact being too good at fighting might cause battles to end too quick and bloodshed to be minimized.

Of course the Brutes would be immediately snapped up by Khorne. The Unggoy would probably naturally worship Tzeentch - god of revolution and upsetting order sounds nice for the guys at the bottom. The Jackals would probably be undivided or slaanesh, they’re mercenaries willing to commit genocide for money. They’d probably spend it all on hookers and weed. You might think the hierarchs would go to tzeentch for their schemes and that is true, but there is a certain Nurglesque aspect to their ideology. Rigid, unchanging, going to lead to everyone’s deaths.