TL,DR version of this post: What if we used two checks, one rolled by the hidden thing vs. passive perception, and the other by the party against a fixed DC once the party is on the right track. I think the results could encourage interesting interaction with the environment, with room for rolling, by avoiding purely binary outcomes.
---------
There are some cool ideas above. I think a good goal is to encourage meaningful interaction with the environment, but making it directed enough that we can avoid the boringness of either exhaustive or automatically successful searching.
To me the important thing about passive checks is that they set up scenes and context. Every trap or hidden object is part of some larger context, and I think passive checks can do a great job of informing the party about the context, without revealing the hidden element itself. If done correctly noticing something with passive perception can be an incentive for more creative interaction with the game's reality. In that case passive perception is spidey sense, but it doesn't skip to the end.
Mechanically, I'm wondering if this couldn't be represented with two layers of checks, but really only one at the table. Namely, each hidden element rolls its own check against passive perception (before the game), and those with sufficiently high PPs find its clues. This provides variety in the process, so that sometimes "easy" traps are missed and hard ones are found. The justification is that passive perception is about taking in a lot of information and coming up with the interesting bits. (This process of integrating over lots of information is what makes passive perception perfect for use as an "average" awareness.) For hidden elements the interesting bits are obscured by definition, so what counts as interesting in this case are the context clues. A trap that rolls a low check vs. passive perception basically leaves a lot of context clues which the party can discover. One that is high does not.
The actual finding of a hidden element then uses a fixed DC against which the players roll. The players' active checks are about finding the specific elements that are the hidden thing, and they are therefore perceiving with more limited scope but in greater detail. Here the player's roll represents the wide variety of relevant details one might catch or miss when searching with such specificity (you find it or you don't and there can be plenty of variation) but the difficulty in doing so is basically a function of the hidden element itself.
I might give bonuses to a player's roll if the context clues put them on the right track. And if they figure it out directly, you can just give it to them without a roll. This encourages interaction with the scene, but doesn't leave the whole thing to guesswork. If they miss the passive check they might still search the correct areas, and the good bits of advice earlier in the thread still apply. I think, though, that you can save a lot of time by letting passive perception guide the players, and setting up the expectation that active perception rolls have a fairly narrow scope.
I don't think this is too onerous at the table, because the additional rolls mostly happen before the session. They also give the DM flexibility to make hidden elements easy or difficult in different ways. Truly devious traps are difficult in both respects, but I think it is interesting if the party suspects a trap but cannot find the actual mechanism. That can really ratchet up the tension. It might also be a good mechanic for PCs hiding things or setting up traps themselves. A level whatever trap might have a set DC to find once someone is looking in the right places, but a more skilled PC can make it more difficult for others to figure out something is amiss in the first place.
Let's consider an example: a drowning trap where an enclosed room fills with water. Before the trap has triggered perhaps the floor is wet from its last activation, or if it occurred long ago maybe their is peculiar discoloration of stones in one corner of the room, or some wood that has rotted away in an otherwise well-preserved environment. None of that really gives the trap away, but it can surely set them on the path to specific interaction with the room if they succeed. If they can't find the trap's mechanism, however, perhaps their passive awareness of it prevents the trap from gaining the equivalent of combat advantage when it triggers. If they don't catch the clues at all, we're in the more traditional searching situation. Even here, however, if clues later come to light (say a trap almost triggers, or does trigger but the mechanism remains hidden) the fixed DC to find the specific thing can be used, rather than using the (apparently very high) roll the trap made against passive perception, as would be the case if these were normal opposed checks.
