I brought a 22x10 rollerboard + laptop bag (my standard carry on) and no one questioned me.

I too spent the night in SIN as I wanted to wait until morning before going into town. There is no JAL lounge and only SATS and Dnata are open 24hrs, so your choices are to:
(1) wander the airport - many places to sit and sleep and things to see
(2) check into a transit hotel
(3) enjoy one of the lounges, like I did

Despite a post on OneMileAtATime from 7/2016, SATS Premier no longer accepts JAL/One World (so they told me). Unless you have Priority Pass, your only overnight lounge option in T1 is Dnata. I found Dnata to be very nice and entered by paying through Lounge Buddy app because I no longer have Priority Pass. Here's a $10 Lounge Buddy Discount code: 9VEHBQAur1 for Dnata lounge if you go that route. You purchase a 4-hour visit and although the front desk agent mentioned the time limit to me, no one appeared to be enforcing this. I stayed for about 6 hrs. Drinks are avail all night (including great Hudson's coffee, served by baristas after 6am) but food resumes about 3am. Worth the $28 I paid!