Why does my acne seem to get better when I am busier and actually taking worse care of my face?

Less is more. Some people's acne is worse when they use irritating astringents or other scrubs. For many people, simple washing with a gentle soap like cetaphil or dove, using just their fingers, is better. And use a gentle moisturizer that is non-comedogenic.
Stress? That is interesting because it's usually the opposite. Most people with acne get worse with stress so it's possible that when you're not busy that you have time to focus or fixate on your appearance which may then manifest as anxiety or stress which then triggers a vicious cycle which causes your acne to worsen. And maybe the products you're using are actually exacerbating the condition.