After a lot of argument and trying to convince, they are now offering me.... Diners Club Privilege!! That too paid. I appeared offended and asked them why they are insulting me. I told them that I once had it and closed it because I was fed up with it, and that it has now become so utterly useless that it is as good as a stain. They said sorry sir, this is the best we can do. As a consolation, they offered to get it converted to LTF after application.
So after giving up trying to get SBI, ICICI and AU cards, I have now given up trying to get HDFC cards as well after trying for two years. Looks like I am stuck with Axis (and Amex) for all eternity now.
Preseverance does not always pay off, you see.