Thanks for the advice, everyone. I coughed up the extra $, and stayed in the hotel. It was a good decision, as I was able to get some proper work and sleep.

For future reference-
I was pleasantly surprised that there is indeed a sleeping couch area in the J lounge. I was previously unaware of this, as it's well hidden in a small passage with a teeny tiny sign. Anyone would have assumed that it leads to some staff area. Anyway, I tried staying there on the way back for half an hour - and it was not the quietest place in the airport. Although there is a lounging couch with a pillow and airplane blanket, it may not be comfortable for a nap that's more than 1-2 hours. It's semi-private though, separated by curtains. Two couches each for men and women. The lights are perpetually kept on. Noises from the outside (as well as the slapping sounds from the adjacent massage room) are very very audible. You need to bring your own earplugs and eyeshades to survive. I did hear that some people do stay there overnight. I imagine it would have been a tough sleep though.