when I was a DM, I struggled with how to Keep a party interested, and amused when they had defeated/solved the room I was running. I have tried several options including small dexterity puzzles (Brainteasers) and such with little success (They only occupy 1 person, and you have to collect them back up, etc)
There's not a "one size fits all" answer to the question either. Conversation might work better for one volunteer than it would another
The Hidden Easter egg idea has a downside. Players have in the past done damage to the set dressing looking for clues, tokens, ducks, and whatnot. Obviously it's not every party, but we've tried hard to steer away from "hidden things" in many regards because of that downside.
Secondary solve options would need to come from Jeff Martin. (By Secondary solve I mean the room has been defeated, and they arrange the props in a second particular order)
As regards the E3 part... I tend to limit two different things you suggest, One being Rotating props. If the players take the weapons in Room 3, we'd need 5-6 sets of them to have them able to be carried to room 5, and then they have to be collected, and ferried back to Room 3. It seems like a small thing, but it's got to be done, and done consistently.
The other part is Reward for creative solves / etc is it starts to deviate from the Consistency that we strive for. the Ideal is to allow a creative group to get a success in a room, but not to let that happen so often that it warps the room as everyone does the bypass rather than the intended solution.
We have had token interactions (like the skulls you mentioned) in the past. Often times they are Subtle, and go largely unnoticed (I had 4 parties do that at Gencon that I know of) As to How often they are built in.. That's a Jeff Question. Even I as an AC don't know about such things till they come up.
-Master Li Lou Bahn, Terror of the East, Master of Shadows, Pillager of the province of Ch'in, Mandarin of the Emporer Shou Wei, Ambassador to the foreign devils of the West, and the most dangerous ninja in all of Greyhawk."cause I'm the only ninja in all of Gwehawk!!!"
2015 Adventure Coordinator for Sable Gauntlet