Dear lax.sea.jnu,
I just did exactly this last week!
I highly recommend the Ambassador Transit Hotel. I have stayed there twice now. You can book online here:
www.harilelahospitality.com
It is located inside Terminal 3 (airside) and costs SGD$100 (single) for a block of six hours (and SGD$25 for each extra hour on top of that). Private ensuite contains shampoo, conditioner, moisturiser, comb, hairdryer, tissues. Room also had a complimentary bottle of water, tea/coffee making facilities and was super clean and perfectly quiet.
There is no pool like the Aerotel, however, you will be in Terminal 3 (closer to your departure gate) and you'll probably want to sleep/shower mostly. The room also gave a complimentary visit to the Ambassador Transit Lounge located next to it so that you can eat something if you don't already have other lounge access.
I hope this helps ))