That simply isn't true. They have support for some very specific areas which they consider of specific importance (e.g. Android), for the rest you're left to rot.
> Perhaps they do not have a corresponding relations team focused on operations support.
This has nothing to do with ops, it's a developer needing a raise in his apps requests quota.
On the other hand, I am happy that even the big G cannot afford to cover all fronts. It means, there is still room for new players to grow and do well in those areas.
If some one came to me saying my employer is saying I am a poor performer and trying to sack me and gave the Google apis's and its documentation as an example I would have sympathies with the employer.
Logins, refreshes, clicks, new things synced, etc... can all update the last activity timestamp.
Kudos for assisting, its just frustrating to realize its needed.
E: If you haven't already done this, of course.
For premium users sync every minute.
Use Indian payment gateways if possible, though Paypal works fine too.
This is by far your easiest and clearest path to monetization, at least that I can see. And it seems you're long overdue for monetization.