I used this company, Santa Fe Relocation, for a move from Bangkok to Ho Chi Minh City, Vietnam, as well as for several local moves within Ho Chi Minh City.
https://www.santaferelo.com/en/contact/our-offices/thailand-bangkok/
They were extremely professional. That being said, I didn't need to have anything disassembled, so I would suggest telling them what you need and asking them if they can do it. They will send somebody around to assess your needs and give you a quote. In my case it was an experienced European lady that they sent, which I really appreciated because, well, farangs understand the needs of farangs better.