Best bet on the timer one would be X minutes to enter the boss room. That means you can fight him as long as needed, and come back and still clear the level. But you can't fully power-up in the current level before facing the boss.
Even that's still EXTREMELY dependent on luck. The game typically generates multiple paths branching out from the starting room in a rather linear fashion, and this would end up not only be about totally randomly choosing the correct path from the very start, but it'd also involve how LONG the path is, the contents of all of the rooms (some take way longer than others to clear) and other things.
Worse, the average time to reach a boss room (or do basically anything else) rises very drastically over the course of the game.
And one way or another, it's pretty much ALWAYS wise to explore the floor first before fighting the boss. Particularly on higher difficulties, you want to be as powered up as you can before taking them on since they're so dangerous. Particularly "major" bosses like the Warden.
Generally I'm always against any time-restriction mechanic in a game like this. I've never seen even a single game of this type *ever* pull this off without it being either A: stupid, B: pointless, or C: just really annoying. Even Isaac, arguably one of the most pure fun games in the genre, gets this utterly and totally wrong in every way.
Now as for the sacrifice room one, I'd be VERY against anything that only temporarily increases max HP and then takes it back later. Nobody likes that mechanic when it appears, and it just leads to items that simply never get touched. It's just too easy to forget to do these things (and no, the warning at the top of the screen wont really stop this; it's natural to just stop noticing it's there after a couple of rooms... this happens in alot of games), and thus you get the frustration of just arbitrarily dying when the effect breaks, because the game's been throwing ten million distractions at you over the last 20 minutes as you explore a gigantic floor. But it gets worse: This is ALSO assuming that the player can even find the sacrifice room. If the game is being stingy on the missiles... which it definitely can... or if the player is just outright on a big floor that has ALOT of rooms with health shards, such an item could be downright suicidal to ever grab. For an item that can kill you, there's too much RNG here. And if they DO find the room, this item essentially would then make it WAY too easy to get the items in there, which tend to be at least a bit OP even just one at a time. It has a very high chance to be an outright broken item in multiple ways rather than just one. But the biggest factor of all is simply that most players would never touch it. It ends up taking the spot of something else that could be interesting and fun.
Now, something else has occurred to me just now regarding all of these things: The rewards. The way the game gives resources to you can be... a little bit of a mess, leading to players running around with like 30 keycards and constantly having 256 credits, or something like that. Heck, JUST within the perks alone are very easy ways to get both alot of keys and alot of credits. These probation items end up only REALLY being of much use very early on; in the mid/late game, they often just dont matter much. So they end up being a very inconsistent mechanic. What might be done to fix this up a bit, and make these stay mostly relevant?