I feel like it shoudn't be a big deal, to be honest. I understand the discomfort, I've been called Aunty by someone my age before and it's totally weird. But it's weird for a second, you correct them by telling them what you prefer to be called, and call it a day. It doesn't need to be this whole thing. 

But anyway, I can understand people feeling weird about it if it keeps happening. In that case, your idea to use da and di makes sense, just to keep it uniform across the board. 

Sometimes it's nice though. Like my mom's students call me Brinda Didi, and the children of people who I call Dada and Didi call me Mashi or Pishi, and I kind of like it. That familial tie establishes a close relationship that makes spending time with them more comfortable. 

In general, I think people are way too obsessed with what people call them or think of them or how old they may or may not look. Embrace it, you are a human and you're going to go through changes, might as well stop denying that part of it. All you have to do it be straightforward: \Just so you know, I am your dad's age so call me Sudipta Kaku, not Dadu!\. And then it's done. You can be even more aloof and take Dadu as a sign that you are the epitome of wisdom (just joking). 

Anyway, since I can bet most people disagree with me, I like your idea of a compromise, Sudipta da.