What are the best ways to travel from Bangkok to Savannakhet for a visa run without using a mini-van?

The key is to fly to a city close to the Lao border, not too far from Savannakhet. You don't want to fly into Savannakhet itself; hardly any flight s (only from Vientiane these days, the Bangkok via Pakse flight no longer exists) and there is no VOA at Savannakhet airport either.

I doubt it's expensive to fly Air Asia to Nakorn Phanom or any carrier to Ubon and then travel the 1.5-2 hours to the border at Mukdahan by taxi or bus and then catch the international bus across the border.

Check if you can just walk in or need an online appointment. They can get booked up well in advance

Fly to Ubon and transfer to Mukdahan.

recommend to go with vip train. better than bus.