How about nodding your head to the people you pass if you’re in the midst of a conversation? At least you’re acknowledging them.
I think, generally, women should greet women, men, men. However, it’s common courtesy to acknowledge another when greeted, and I think it’s just plain rude to lower ones head and pretend to be deaf just because someone has different standards and greeted you. An effusive “how do you do?!” is not necessary, but a quick “good Shabbos” so as not to be rude? Common courtesy. It’s derech eretz to be a mensch to others. If you respond “good Shabbos” loud enough for the greeter to hear as you continue walking away, it’s pretty clear t’s meant just as a response.