Goodness, as you point out in your OP, lot's going on here.
Hmmm. Well, when I was in my final year at university, my dm went into hospital, and I went home and helped out. And, boy oh boy, do I regret it now. Mainly because I know now, and knew then, that I was falling for the implicit assumption that it is a daughter's role to drop everything, and help out.
There is so much embedded in that, not least the whole "love-work", female thing. It's hard to untangle, because some of it is good, and nurturing, and some of it is so, so bad (women have no lives of their own, and should drop everything for others).
I have also gone round and done a day's cleaning at a friend's place, when she was having a rough time. I feel OK about that, because it was only a day, and I was quite aware of my reasons for doing it. In a way, it was more symbolic than truly practical (how much cleaning can you do in one day?), so the point was to demonstrate care. And it was limited (just one day), and we were both, very clearly, on the same page, ie. my friend really wasn't going to be cross about lack of on-going cleaning, etc.
So, thinking about your situation, I really don't think you can make an on-going commitment. It's not feasible. You could do what I did, and do a, symbolic, day - but will it be recognised for what it is, and accepted positively?
I also really do hear what you're saying about resenting the equating of cleaning with love. There's a potentially sexist subtext there, that you may be trying to avoid (rightly). On the other hand, nurturing is devalued (and how) but, damn, we all know how important it is, and it shouldn't be devalued. And it is devalued (and rendered invisible) as "women's work". And here you are, in a situation where it is clear how much value it has, binding love, and life, and the practical, and the emotional.
So, a question: do you have brothers? Have they been asked?