Note there are two seemingly conflicting strategies here. One is to solve part of the problem, focusing on it for a given time, trying to jumpstart a success spiral. But how would you differentiate this from bikeshedding? How can you be sure you're not focusing on irrelevant things?

You can't. That's where iterating comes in. even if you do spend 20minutes solving the leaking tap in the bathroom, which is maybe the most irrelevant problem, you only killed 20 minutes.

I would suggest hamming style questions too - to ask "what is the biggest problem?" a few times. Not just listing out the things that are bugging me.

This strategy is not going to work the same if you have a sharp deadline - i.e. an assignment due tomorrow. In a problem-situation with no deadlines - try to work on any one problem for a period of time will work on that one problem.