Hey Vippy, just played, and I'll leave some feedback here! By the way, my highscore was 82, let's see if someone can do better (I'm sure someone will do, though).
The game is very simple, and plays well, so there's not a lot to say about it I guess. As you said, the games needs more polishing, and then I believe you could iterate over and over to make it better. Anyway, I think something pretty cool to add would be if the clock hands interacted with each other: like going back on the minutes would make the hours hand go back as well, or making the hours run faster would make the minutes run even faster. I believe whis would maintain the game minimalist style but adding more depth.
For example, in some parts of my gameplay, The minutes hand (the one I was using the most) was directly opposite to a incoming clock, and the hours hand was barely protecting Jimmy from that clock. If I had to let go of the minutes hand, other clocks would them become a problem; however, if the hands were connected (as in real life), I could move the minutes hand a bit and the hours hand would move enough to destroy that incoming clock.
However, maybe that was the approach you were looking for: making the player do various rapid decisions to change which hand to focus on to keep the alarm clocks away, while also being conscient of the consequences of letting go of the current clock hand. If this was the case, then well, good job! I believe you managed to do it, and the above was just my opinion.