Thanks so very much, everyone!
I've written to the Eaton Smart at T3 to ask if we can access the T-Lounge by paying a fee rather than booking a room for the minimum 5-hour slot. We do have a pretty long flight to DEL, with a stop in Brussels, so I was hoping to be able to freshen up before we both land in Kolkata and are surrounded by family, but not necessarily sleep (I hate short naps).

For everyone's reference, here are the room rates:
5 hrs: INR 3,900
6 hrs: INR 4.650
7 hrs: INR 5,400
8 hrs: INR 6,150
Overnight: INR 6,900

So I'm guessing it wouldn't be a bad idea to call the various lounges and ask for their fees? I'll post back here if/when I get the rates.

Thanks again for everyone's advice!