I'd suggest getting a room at the airport. The Crowne Plaza is excellent and is landside. I assume you don't want to leave any luggage there and will be taking your hand luggage with you to BKK. So depart SIN for BKK and when you return have dinner in the lounge (if you are still hungry) before exiting customs and checking out Jewel before sleeping at the Crowne Plaza.

Technically you could go back into town but that would be a wasted two way trip. IMHO night time is the best time to explore Singapore so I'd be doing that after returning from BKK. Things tend to be pretty dead in the early mornings.

Can you come and go as you please through the border? I don't know. I've gone landside for pretty short stays in the past without a problem but I've never entered Singapore, a few hours later leave (for dinner), then go landside again to sleep etc etc.

Another option is upon return from BKK go landside to do your exploring and if that is likely to go until midnight come back airside and book a transit room (6 hours). Then you can spend as much lounge time as you like and even hop from terminal to terminal.