I'd expect them to be on VN414 (1025-1635) or KE480 (1220-1840) on 30 Jun from Hanoi to Incheon.
Looks like an evening leg in Seoul. If they were connecting to a different part of Korea production would release them for an earlier flight such as VN416 (2340-0550) so that they could race in daytime.
The last Pit Stop is always relatively short. (TAR 27 had ~17h, TAR 28 had ~10h.) Expect them to depart Korea on 1 Jul, crossing the international date line to be back in the US by 1 Jul. Seoul has direct connections to plenty of US cities, including Anchorage, New York, Detroit, Washington DC, Chicago, Los Angeles, San Francisco, Seattle, Las Vegas, and Honolulu.