I wouldn't expect to be able to check bags through on separate tickets, especially if the airlines aren't partners or one is a LCC. However, the transfer desk (airside) at SIN might be able to retrieve your bag and tag it for the SQ flight, so that you could avoid going landslide to check in.

Don't worry about changing terminals as SIN is really one big terminal with different zones that were build in phases. There's an airside little train/tram or you can walk, although the tram is infrequent in the middle of the night.

Similarly, even if you must enter and go landslide to retrieve and recheck the bag, it's not a big deal. This is an efficient airport. More importantly, since you're departing on SQ, you don't need to wait for their check in counter to open. You can check in at the airport starting at T-48 and then go airside to enjoy the airport: free movies, the butterfly garden, koi ponds, lots of shops, interesting F&B outlets, as well as the excellent SQ lounges with very nice showers as well as F&B. There's even a big slide (fee to use), IIRC landslide in T2.

It sounds like you don't want to explore downtown, but nevertheless, I'd still allow lots of extra time because you have two tickets. I also would avoid a carrier with once a day service DPS-SIN unless they interline with other airlines. This would exclude some LCCs from consideration. It's not worth risking a long haul SQ J ticket to save a few dollars.