Hi there, there will be live aboard's running from Phuket. They will probably go via the Similan Islands up towards Burma.
Personally I think you would be better off price wise leaving from Ranong further up the coast. You will then be able to see some of the Similans and then head up to the Banks.
I have dived the Similans and it is first class and have only heard good reports about the Burma Banks.
Yes. Liveaboards go from Phuket & Khao Lak to Similan Islands and Burma.
However, Burma trips from Phuket & Khao Lak are likely to be long trips 5+ days. For shorter trips then better to go from Ranong - company that springs to mind is Smiling Seahorse (no afilliation).
Also, I have heard from divers that Burma has had a lot of blast fishing and in some places there are very few fish because of this, Apparently the macro is very good and different to Thailand.
Other options for you could be to look into visiting the Surin Islands or Richelieu Rock - which is still striking.