I have booked a transit hotel at SIN for Dec this year. I wrote an e-mail explaining the situation that SIN is our final destination and due to the late arrival we'd like to stay in the transit hotel until the next morning.

This is the e-mail I got from the transit hotel:

"Since you will be going into the city after you check out of the hotel please see below:

On arrival you MUST NOT collect your luggage.

If you Clear Immigration and collect your luggage you will not be permitted to re-enter Departure Transit Lounge/Mall (Restricted Area) where you just step off the plane.

The Transit Hotels on Level 3 are located in the Departure Transit Lounge/Mall.

Have a hand-carried or overnight bag for your short stay in the Transit Hotel.

The next morning after you check-out of the hotel, collected your luggage at the Lost & Found Department after clearing Immigration on Level 1.

This department stored all luggage not collected after all flights arrival. Clear Customs and you will be in Arrival Hall."

I'm not totally comfortable with this (leave our bags for a whole night) but this is kind of a cheap and easy way to spend the first night.