I don't share your concern about DEL. Chaotic? Compared to what KL??
Delhi was my PF. I stayed in the embassy district for 5 nights, and I had loads of things to see & do. Recommend Gandhi Library (NB not the Museum:
http://www.gandhilibrary.org/
BOM is also very interesting. Lots of reasonably priced accommodation. We checked out Bollywood.
What about combining BOM with a trip by rail to Cochin?