Measuring time was the primary factor in creating a sort of Exploration Turn in that arena-esque Megadungeon I've mentioned recently. The "arena" is a cylindrical cavern with several buildings built into the wall and a castle in the middle of the floor. I'm counting "passing through a building" or "exploring a room" as a turn.
"Passing through a building" means exploring through with nothing of consequence happening, except a couple combats or similarly brief encounter. (Actually running through a building just takes a minute and gets wrapped into the previous turn or the next)
"exploring a room" means spending a substantial enough time in a single room: dealing with a trap, solving a riddle, whatever. What your rule would require 30 minutes for, mine requires only 10.
Although it remains more abstract than what you propose, it flows well. It gives them a chance to decide a room is worth checking out and do something before that random encounter is rolled for, yet knowing there will be a check if they do something.
I kinda think your proposal would work better with 5 minute turns (and 10 minute encounter checks), is what I'm getting at.
The first round would be for checking out the room for anything worth checking out (locating a hidden door, etc), and then with the second round they'd get to decide whether to play careful (check the door for traps, but spend more time) or barrel through the door, risking a trap in exchange for moving on before the random encounter check.