Although I do not always have much respect for UK consular services, I cannot imagine they would be unaware of the countries that will accept their emergency passports for entry. More of a problem, I think, is liable to be the Thai consulate in Savannakhet, and their policy on stamping visas into such passports.
At land borders, care is needed on this. It should be possible in general (as should transferring the entry stamp at Nakhon Phanom immigration) but transferring stamps at minor land crossings can be tricky, especially if senior officials are not available. Better, as I suggested earlier, would be if the OP could fly out from a Bangkok airport. There, it is certain that they would be able to promptly accomplish what is necessary.