Yeah, as Chris says, having one ticket to check baggage from departure airport to final destination makes changes WAY easier.
Timing could be quite tight. Again, as Chris says, if you can do it anywhere, Changi is the place. An amazing airport. I'd be tempted to grab someone from customs service as soon as you can, be super nice and outline the tight connection. They may be able to assist in speeding you through and getting to the front off queues. If, on the other hand, they are relaxed about it... there's your cue!