Another very underrated option with UR is booking with KE. You can be virtually guaranteed to find KE F space for the TPAC from JFK and then it's an A330 down to DPS.

A big caveat, you can only book for immediate family members and it requires you to fill out a form - so you will run into problems if your #2 is a SO who you aren't married to or a friend.

I'm not seeing much availability for DPS - ICN - JFK but am seeing basically wide open availability for JFK - ICN - DPS. Looks to be 95k/person though the website seems to be having some issues (and there is a warning at the top to this effect) so I can't actually click through and relay flight details.

What AMEX do you have? If you have Membership Rewards you should be able to transfer, if you don't, the best option (if you don't want to pay fees) is to grab the no annual fee AMEX EveryDay. It has a nominal 10k bonus (occasionally 15k and rarely pops to 25k) but it's better value is that it is an MR earning card and as long as you have one MR card, any MR you earn from any card is maintained and can be transferred to MR partners.

Something to note about SQ. I don't think there is any F to DPS so the website won't show any F availability for NYC - DPS and you'll need to call to book say JFK - FRA - SIN (SQ F) - DPS (SQ J) since the website doesn't allow J/F mixed itineraries. That also means you need to search just to SIN for F and then separately search for the DPS flight.

One last thing, SIN - DPS and even BKK - DPS are relatively short flights so you can search to those major gateways and buy a separate Y ticket and you may find more options (for example, UA will let you route via Europe to get to BKK so you could conceivably do JFK - FRA - BKK on LH J/TG F, etc.)