Best thing is to wait until on the aircraft to HKG from LAX or DFW and then pay for wifi access then start looking for tickets to DPS. Possibly look connecting through KUL or SIN for lower costs. Might cost more waiting until last minute but you would lose out if you could not get to HKG on the day of your paid flights.
Also, look at flights from China (PVG or PEK) as you can have a transit without visa IF YOU HAVE CONFIRMED SEATS out of those cities, just in case flights are cheaper. You would only be able to go to DPS doing that, looking at other routes back.

Chose LAX or DFW whoever has the best number of seats on the days you want to fly.
always have backups like SYD/AKL even though flights from DPS to those cities are more if AA flights have seats its better to get home then stuck somewhere.