In May, I took a 120K DL SkyMiles award ticket trip on DL and SQ: ATL-LAX-(TPE)-SIN-BKK. I left it as an open jaw, returning ten days later SIN-(NRT)-LAX-ATL. I spent two days in BKK, then Mr. Megatop and I flew on a paid Y ticket on SQ (they have a "Two-to-go" program that discounts tix if you buy two at the same time) BKK-SIN-DPS. Spent five days in Bali. Then went back on the same paid Y ticket DPS-SIN and spent two days in Singapore. From there, I picked up my return to the US and Mr. Megatop went on home to BKK.

For your trip, I would have tried the SQ or TG nonstops EWR-SIN or JFK-BKK. Both have a premium economy product, which is about as good as DL domestic F. I saw that you couldn't buy the paid C tickets for anything reasonable, unfortunately.

When I was booking, TG had only one flight per day BKK-DPS. The times weren't terribly convenient and we wanted the stopover in SIN, so we took SQ. Tourism demand in Bali seems to be picking up a lot, so TG may have added flights, especially now to work connections from the "New York Express."