Everyone runs shroud on normal, why? because there's no benefit to running anything else. Aside from the odd favor run of elite shroud nobody runs anything harder because there's no reason not too.
Adding a extra chest with 50% chance at a large ingredient (Like part 4) on hard and an extra chest with a 100% chance of a large ingredient on elite would give people a reason to run the shroud on something other then normal
Think of raids like hound.... there's actually a decision to be made before entering. You can go for the easy completion on normal or go for hard or elite and have a chance for an elusive +3 tome.
Note: My suggestion is not necessarily the extra chest, its more a suggestion that shroud needs an incentive to be run on hard and elite, the chest idea was just and easy way to accomplish this. If anyone else has any suggestions on incentives that should be added post them and i can add them to the main post along with mine.
Suggestions:
Maybe instead of extra chests (do we really need more than 12?) have the ones that are there now have a chance to drop Greensteel ingredients (Chipmunk Funk, etc.) and/or +3 Tomes, and additional chances for large mats (as OP suggested, guaranteed in Part 4 chests on Elite)
-PNellesen
~Sky