If it helps anyone else, just some minor comments on opus' excellent report:

1) You can change US$ into Malaysian Ringgit in Singapore. Whether there is a currency exchange open is another question. For instances like these, you can always use an ATM in Malaysia. Or pay the taxi driver in S$ or even US$. S$ they'll definitely take in JB (but definitely not at a good rate)

2) The regular Singapore taxi will not take you into Malaysia. The taxis that will are available at Rochor Road bus interchange as described. They take S$ and will take you to the bus terminal in Larkin.

3) Bus services in Singapore generally stop at midnight.