Terminal 1 is the Transit Hotel next to the pool and exercise room and by your United gate. I think that would be your better option.

Website : http://www.airport-hotel.com.sg

(from last month)
Ambassador Transit Hotel
Singapore

Listed below are our Room Rates and Conditions:
Single Occupancy is S$57.75nett, Double/Twin Occupancy is S$64.70nett and Single Budget Room (Common Showers and Toilets) is S$40.45nett. Triple Occupancy :
6 Hours Triple Room - S$ 86.65nett
7 Hours Triple Room - S$ 114.35nett
8 Hours Triple Room - S$ 136.30nett
9 Hours Triple Room - S$ 150.15nett
Room Rates quoted are based on minimum charge of 1 block (6 hours). Extension per hour is at SS13.90nett. Additional person/child/bed SIN$21.95nett.