I have the basics (.in) extension, server in India and the entire site uses Indian specific currency, and markup that shows its clearly just for Indian serps. It's https etc. It just doesn't seem google has much interest in the indian serps being country specific.

You've got the basics covered and that will give you a bit of an edge in the Indian search results, but it's not a free pass to high rankings, you'll still need to compete with the other English-language sites (like from the UK) in other ways like a good user experience, trust and backlinks. I think it's important to have country-specific backlinks, too; a signal that people in India specifically value your content.

It might also help if your site's content includes some place names -- regions of the country, major cities, etc

Sadly we have that, full state and federal laws for the majority of the states in india. A few years back google favored india specifically, but changed them to favor UK serps in India for our niche I believe for the most part.