Yes, thank you! Your second point is what I meant by "time isn't sacrosanct," and your third point is what I meant by "an analogue of time." I'm glad it makes sense in your own words.
I guess "urgency" and "trepidation" don't quite map to what I mean. Let me try a model I've used before. Let's imagine you're playing on a game show, kind of like Deal or No Deal. There are twenty briefcases in front of you, and one of them contains $1,000,000. Now, I could set you off onto the briefcases, but as it stands, there's no tension to the game. You can just check each case, one by one, until you find the right one. Now imagine I set the following Limits on your search:
1. You only get 1 minute to open as many cases as you can. (Or you get until a big meter drains, or until the sun sets, or whatever). Imagine this game in your head. How does it feel? The moment I say "go," what are you going to do? You're going to race to the closest case and start prying it open! As soon as it's open, and you know it's a dud, you're going to race to the next one. You can't spend any time looking at the briefcases, because any time spent measuring or analyzing the cases is time you could be spending opening them. That's what I mean by "urgency."
EDIT: Now, as you're imagining this, look up at the timing mechanism. It says some time, or the meter is so full, or the sun is at such a position. Now, as much as you hate to do it, stand still for a short amount of time. Look up again. The timer has lowered, the meter has drained, and the sun has lowered. You don't need a numerical value to understand that your situation has worsened significantly.
2. Instead of the previous example, I say you can only open three cases. Now how do you feel? When I say "go," do you immediately jump to the first case and pry it open? No, that would be a waste of one of your three cases. Instead, you're going to stop and look at each case super-carefully. This one has a red tag on it, and you've heard those are slightly more likely to be winners--but this one over here is scuffed on the bottom. Is that because it's heavier with all the money, and the producer dragged it on the ground? Maybe it's the one farthest away, or maybe the producers wanted to be sneaky and put it right next to you, knowing you'd overlook it as "too obvious." That's what I mean by "trepidation."