I wouldn't overthink the terminal transfer piece, unless looking a Jetstar or Air Asia who fly from Terminal 4. Otherwise it's 5 mins+/- 2 mins difference between staying in the same terminal vs moving between terminals.

If you can't through check luggage from your point of origin, if you take SQ, you almost certainly will be able to get your luggage retagged by presenting at an airside transfer desk.

For Scoot, you will have to clear immigration (allow 30 mins, probably much less) and recheck at the self serve check in facilities. Returning through immigration take less time than security at most airports. (security is done at the gate in SIN - so whether you stay airside or have to go landside, it makes no difference for security).