What might be helpful is if you see what airlines fly directly into DPS and from what cities. Wikipedia is usually a good resource for this:
https://en.wikipedia.org/wiki/Ngurah...tional_Airport
Then, you can see if it's a simple flight from a major gateway (SIN, HKG, NRT/HND, ICN, TPE, etc). Hopefully you can get to one of those with no more than one stop at a US gateway city (LAX, SFO, SEA, etc). At best, from STL, it's likely a 2-stop trip. The overwater segment is the key. Your domestic US trip is relatively short. Depending on whether you connect in North/East Asia or Southeast Asia, that segment can vary in length. For me, the driver is usually getting the longest leg of the journey on miles/points and filling in the connector flight. If the connector flight isn't available in premium class, I'm usually OK with a mixed cabin award. Or, just buying a cheap one-way flight, if such things are available.