I know it is something people do every day at SIN, but I would not be comfortable leaving checked baggage at the claim and hoping it made it to the airline baggage office the next morning. That's a personal thing, obviously many people do it without issue. Last time I was at SIN on that midnight arrival from NRT, I just went through immigration, got my bag and went to the Crowne Plaza in T3. It was only $50USD more than the transit hotel would have been for that night, got a full night sleep and took a taxi to the Pan Pacific in the morning.
This should solely be a financial decision in my opinion, all the other stuff you mentioned will be no different whether it is done at 1am or if it is done at 9am. If the hotel you'll be staying in for the other nights in SIN is significantly more expensive than the transit hotel would be, then just stick with the transit hotel (or explore the Crowne Plaza's cost) and head into town in the morning.