I'm planning a week's trip to Singapore and Kuala Lumpur. After spending three nights in Singapore, I'm planning on spending two nights in Kuala Lumpur before returning to Singapore for my final night. My flight out of Singapore departs quite early on Northwest Airlines.

I was considering taking the flights on JAL to/from KUL, as mentioned in another thread.

17MAR JL 721 SIN 0640P KUL 0740P
19MAR JL 722 KUL 0900P SIN 1000P

20MAR NW 012 SIN 0610A NRT 0140P

I was thinking it might be a good idea to book those flights, then stay my final night in the Singapore Transit Hotel in Terminal One. Am I correct in assuming I would arrive in SIN, stay overnight in the hotel, then check in for my Northwest flight (presumably at a transfer desk?) and not have to go through immigration/customs-- staying in the sterile area of the airport the entire time? Does this sound like a good plan or are there better ways to do this trip?