If you have not already booked may I concur with other posters and suggest:
Check-out of your Singapore Hotel.
Leave you main bags with the Bell Desk
Take a small carry-on and book the First Class AeroStar Bus [its worth the US$6 more]
Stay a Night in KL
Book a room at a 3star Hotel with
www.asiarooms.com eg the Ancasa US$47 or 4 star Dynasty US$57 inc all taxes and a full breakfast.
Late afternoon flight First Class with MH from KUL
Arrive at KIA early enjoy Afternoon Tea/Dinner in the Lounge
Relax with Vintage Champagne on the flight