The thing to keep in mind is that the Thai alphabet is an adaptation of the Khmer script. So the original Sanskrit and Pali values were already distorted to fit Khmer (particularly to match the traditional vowel phonation now found in some outlying areas - if Pol Pot didn't cause destruction of those areas). For its part, the Thai alphabet fits the language well.
As for Lanna - that's an offshoot of the same Mon script which also gave birth to the Burmese script, and also ultimately Khmer. It too could work, since there are sounds in other Tai languages that are either not represented or are awkward to represent in the Thai alphabet; at the same time, there are conversely also sounds which exist in Standard Thai which are not represented in Lanna, but which could be invented or modified if need be. It's possible.