This was surprisingly fun and despite the control issues, is something I'd play outside of a game jam, so well done! I liked the feeling of speed - when under time pressure like this and having to search a large-ish map it would be frustrating if it took more time to get from one side of the map to the other. For me, it might feel better with a slight acceleration curve and some niceties like coyote time, but the speed is good as is.
I really liked the "in-level" ui; somehow it did a lot to add to the atmosphere of exploring the level. I never ran out of time, so while the timer was nice to add a little bit of pressure (and a 'score' at the end), it didn't feel all that relevant. Maybe you could experiment with not having the timer reset on the player's death and see how that affects the feel of the game.
Overall, very nice!