I could not find the landside hotel either, so will stay airside, arriving T3 just after midnight on UA and continuing on in the late morning with Air Asia T1. As a side note, I did try the airside hotel at SEL and it was great, spent about 6 hours there waiting for connecting flight.
There is no transit hotel landside. Low cost accommodation in SG are not close to the airport.
Yes I notice the Crown Plaza, but way way more expenisve, for the few hours I need to sleep they want 324SGD

, no way am I going to spend that kind of money.
That is the going rate for a CP level hotel in SG. If you don't get a day out of it it is not good value.
BTW if your plans are set it is a very good idea to book online for your stay at the transit hotel to make sure that you will get a bed/room for sure.
I have seen walkups being told they are fully booked especially during the late arrival of the UA and DL flights.