I usually go by BA to HKG or SIN when going to Vietnam.

From SIN, Jetstar har cheap tickets for the 1,5 hour flight to SGN. The flights alight pretty well, but you risk for forfeit the ticket if there's an irrop. You may want to build an itinerary with an extra day in SIN on the way back.

From HKG the cheapest option is usually United to SGN. The outbound flight line up pretty well. The return flight leaves you in HKG for 13 hours, but that's plenty of time to explore HKG for a day. And BA and UA has a baggage interlining agreement, so you can through check the luggage all the way through both tickets.

Can't speak for BKK.

Great news about Finnair to HAN, btw. ^ Thanks for the info.