Maybe you could have set time limits for each level, and then have a grading system at the end?
So if your overall time is more than 3 minutes you get an "Okay" ending, do it in under 3, you get a "Good" ending, and then the fail state of running out of per-level time exists still?
Its a neat premise, it definitely just feels like a pain to wrangle - but you certainly did a good enough job!