Hi i can only respond with my own experience to what I asked earlier:
I arrived Spore on time on my ANA flight from Tokyo, I found the Transfer desk and got my boarding pass for my flight from SIN to BKI on SILKAIR. Since my bag was checked in all the way from Vancouver to final destination BKI, I did not have to worry about getting checked bag and clearing customs.. So I stayed airside and 2 hrs. layover was indeed enough to make the connection at Changi. Both arrival and departure were at T2.
In your case T2 and T3 are connected via a frequent tram service...I believe you can get find your transfer desk and still remain airside between T2 and T3.
I did experience a moment of panic when my bag did not come out on the carousel...same with 2 other guys who came from Munich via Spore...and then as we were making our claims to the airline agent...our 3 bags slowly came out!