Thanks. I read through those (extensive) threads and could not find exactly the answer I was looking for, whether I could stay overnight airside at BOM if I was transferring from an international flight to a domestic flight that nonetheless left out of the international terminal. I decided to keep my Hyatt reservation and was not unhappy - the Hyatt Regency was a perfectly comfortable place to have a drink and a nap before getting back to the airport and the process of getting to my flight at Terminal 2 in the early morning could not have been easier.

For future information seekers, my best guess is that it is not possible to stay airside in this instance, as the international transfers desk was before passport control (and as my next flight was domestic that wouldn't do), but I'd add that the airport staff at BOM was generally very reasonable and that they were happy to offers solutions like, "if you don't need the immigration desk just walk around it," which makes me feel like if I had asked around a solution might have presented itself.

From my cursory glance, overnighting landside at T2 would have been possible - there were a few very basic shops, etc - but not particularly pleasant. I didn't
actually notice where the lounge entrances were but that information is definitely available elsewhere on this board. Airside it looked like any other airport that hadn't been recently renovated.