I recently did the SIN-NRT-EWR you are proposing on NH/UA and had enough time to connect, with probably 30 minutes to spare before boarding began on UA. The gates are relatively close together and you just have to clear security at NRT, which has a special area for connecting passengers.

I would expect that almost 2 hours is more than enough at SIN, but don't have personal experience.

Good luck with all the traveling...I don't envy you the jetlag! It took me a week to get over mine.