Things ended up working out pretty well. I went to the SilverKris lounge on arrival from JFK (before customs). I explained the situation to them. They gave me a locker key so I could store my carry-on until late that evening when I returned from Jakarta. They also spoke to the baggage people and asked them to hold my suitcase until I returned in the evening. The ticket people also took care of reissuing my rtw ticket while I was in the shower.
All in all, very pleasant and efficient.