Next week I'll be traveling on SQ from JFK to SIN in first class. The flight arrives in SIN around 6:30am. I'm connecting to an SQ flight to Jakarta that morning at 10:00am and returning the same evening. I'll spend the night in Singapore. I'll have one checked suitcase and 2 carry-ons (a rolling case for my computer and change of clothes as well as a briefcase).

On arrival I'd like to shower, shave, change. Since I'll only be in Jakarta for the afternoon, I'll only need to take my briefcase and want to leave my checked and 2nd carry-on at SIN.

Questions:
Is there any way to leave my checked and carry-on bags at SIN without clearing customs and just pick them up on return that night?

Assuming I do have to go to customs and get my bag, what is the best strategy? Can I get SQ to hold my bag while I use the lounge facilities. This would allow me to bring my carry-on and checked bag to the left luggage at the same time. If I go through customs from my flight, I'll have to pick up my bag, go back through immigration to use the lounge, and go back out to the main terminal to leave my carry-on.

Appreciating the advice of those more experienced than I.