In the "crazy idea that probably won't survive past this post" department...
I still like the previously mentioned idea about having some of the game elements having visual elements that integrate with the gameplay. It would be neat if this could persist through to the temple as well, but how to enable that? As I mentioned previously, in a much earlier version, the temple was assembled from a series of room cards, each of which showed a room from an adventurer's perspective, along with several exits and perhaps a testable "feature", like a rope or a pressure plate. Imagine that the temple is constructed as you explore -- you look at the card, place it on the table, pick an exit (let's say you pick "West"), draw a new card and place it to the left of the room card you had previously explored. So yes, somewhat like the most recent version, this temple would be randomly assembled. However, also like the most recent version, your search through the temple isn't a completely random walk: if you've accumulated the right clues, you can know what sorts of features you are looking for, eg a clue might tell you that pulling a rope will open a hidden wall to reveal the map room.
Here's the first departure from the previous version: in that version, there are 8 temple tiles (cards), each of which depicts 1 of 8 features; in this new version, there would be many more cards, and each feature would be present on multiple cards, BUT would be somewhat more overt on some cards than on others. For example, there might be several cards that have a "rope" but on some it's right there in the foreground, while on others it's very hard to see. This slightly abandons the conceit that there is one and only one "solution" to the temple -- in this version, whenever you notice a rope on a room card, you declare that you'll be testing the rope, and if a rope reveals the map room, then the rope you pulled was the "correct" one -- the game makes no distinction between them (*). Since multiple cards may have the same feature, you may want to spend some time scrutinizing each card to see if you can find the feature you're looking for lurking in the shadows of the artwork.
But how do you deal with the problem that this creates, whereby the longer a person looks, the more likely he is to find what he wants? There are two possible ways: the first is to add a timer. This is boring and uninteresting; in game design, it's always better to steer your players with incentives as opposed to limitations. The second is the crazy idea part -- make the temple a real-time free-for-all. To wit, players are all simultaneously exploring the temple. So while you're looking around in the "Treasure Room" hoping to find a hidden pressure plate, the other players could be frantically hopping from room to room, trying to catch up to you, or exploring other aspects of the temple.
This will create LOTS of issues; here are just a few:
1. Originally, players could enter the temple at different times; if you discover the temple and want to make a run for it on limited info, you can, but other players can linger outside the temple hoping to acquire more info before coming in after you. That's easy to emulate here; players announce when they're ready to enter the temple, and only after everyone has entered does exploration start, BUT, for each additional turn that you spent outside the temple relative to another player, you must wait 1 minute before you begin exploring.
2. Movement from room to room could be quite chaotic. To slow this down a bit, maybe each player must count to 4-Mississippi before passing to the next room, so you can't "sprint" across the temple simply by flipping cards. Challenges and traps are probably also a natural way to force players to slow down.
3. Vicarious exploration: This could actually be helped in this scheme; you are the only one who is allowed to look at the card for the room you're in, and when you leave that room for another, you place the card face-down on the table. (Not sure how to resolve having multiple people in the same room at the same time).
4. Rules enforcement: This is the toughest part; how do you guarantee players are following the rules regarding challenges, solution card lookups, etc, when everyone is going through the temple at a mad dash? Typically oversight from other players is the most reliable way to ensure that a given player has complied with the rules of a game; this becomes a challenge when play becomes simultaneous. Maybe some events pause the action temporarily while a given challenge or lookup is being resolved.
5. What about the enemy? Not too sure what their role is; the most obvious thing is to make one of the players be "the enemy", but I'm reluctant to go that route.
(*) If this turns out to be truly thematically unsatisfying, we could always introduce an action-at-a-distance effect, eg you pull the rope and look at the solution key for the "rope" feature, and it says "Map Room = Crypt", and now it's revealed that the "Crypt" room card is the map room, so now you have to go and find the crypt, or get over to it if it's already been revealed.
I think this is ultimately a different game than Lost Adventures, unless the whole rest of the game also became a real-time game (which could be cool as well, but likely too chaotic), but it would definitely successfully simulate the mad dash through the temple in a satisfying way.