Invisible rolls
A potential work-around might be to have OTHER players make secret rolls...for instance, if you have Players A-F, and you need to do a loyalty check for vassals of Player A, you ask Player C to make a secret roll...tell him how many dice to roll. You'd need some kind of short-hand they could enter in the 'purpose of the roll', perhaps, so you could keep straight whose rolls were intended for which player's vassals, but if players aren't rolling for their own people, the element of surprise is maintained when the results are revealed.
You still need to tell people when to roll and all that...but you're freed of the onus of actually having to make all of the rolls for every player's various groups of vassals. Not the most elegant solution, perhaps...but it kind of accomplishes your purpose of freeing you from rolling everything and keeping the results secret from the player who's affected by the rolls. And if you shuffle around who is rolling for whom, players are less likely to be able to puzzle out whose roll they just made...especially if you incorporate a few 'fake' rolls that don't actually apply. It's the closest thing to a double-blind I can think of off the top of my head...they're not told who they're rolling for, and they don't know which rolls actually count, so even if they figured out who they're rolling for, they still can't be sure of what, exactly, the results they get are supposed to mean.