I did this in Terminal 3 in May, arriving on SQ and departing on TK. It turned out to be incredibly quick and easy, even with checked baggage. The great ground staff in SIN were happy to tag my luggage to my final destination and print my onward TK boarding passes.

On the arrivals level, there is a transfer desk before passport control. I assume they can sort a boarding pass if you don't already have one, but they just pointed me to the one immigration agent standing at the podium nearby. He looked at my passport and boarding pass, checked it against a printed list, and then waved me through to the escalator. There is a deserted security checkpoint at the top of the escalator, and behind that is the departures gates. The entire transfer process took about 5 minutes.

On the return journey, I had checked in online for the SQ flight departing CGK, but I was unable to get a printed boarding pass. The electronic copy on my phone (not a true mobile boarding pass in the SQ app, but rather the emailed PDF that you are supposed to print at home) was fine for the immigration agent at the transfer podium. The guys at the security checkpoint seemed skeptical at first, but they decided it was OK after talking among themselves for a few seconds.

In both cases, I did go early to the gate for my departing flight, show the agents my luggage claim check, and reconfirm that they knew I was in the departure area.