According to the references
 Hammerdalsmålet, Vidar Reinhammar
 Klövsjöord, Gösta Edlund et al
 Orlboka - Ordbok över jamskan, Bo Oscarsson
the adverb 'so' is in the Hammerdal dialect [sɞː] (northeast), in the Klövsjö and Oviken dialects [sæː] (south), and in the Marieby dialect [sɑː] (central). Apart from these examples, a common pronounciation is [soː] as in Swedish så.
The most fundamental axiom for the creation of a Jamtlandic orthography is that one must find a unified spelling (using the alphabet defined earlier) for every word, at least those that can be traced back to Old Norse. The adverb [sɞː]/[sæː]/[sɑː]/[soː] 'so' can be traced back to Old Norse. According to Svensk etymologisk ordbok, Old Norse had svá [swɒː], svo [ swo] and so [so] with successive degrees of phonological simplification. Note that Swedish så comes from Late Old Swedish so rather than "sá", and (classical) Nynorsk and Faroese have so.
Let's analyze the Jamtlandic instances above of 'so', i.e., looking for the (most relevant) etymology of the word.
Hammerdal dialect [sɞː] is only consistent with an etymology *su. Page 20pp in  reads:
"Långt ô i hdm svarar mot:
a) gammalt kort u. [...]
b) gammalt kort a framför ändelse med u. [...]
c) gammalt kort å framför ändelse med u. [...]"
Note that ô and å refer to [ɞ] and [o], respectively. Clearly, b) and c) are impossible, which only gives the option a), i.e., an etymology *su as claimed.
The [sæː] in the Klövsjö dialect is trickier. In this dialect, according to , old short u has consistently become [ɔ]/[oː], so the etymology *su is a bit more difficult to derive. I think [sæː] is a secondary stressed version of an unstressed [sɐ], which in turn is a derounding (and slight fronting) of an unstressed [sɔ], with a stressed [soː] consistent with an etymology *su.
It's my firm belief that the Marieby dialect [sɑː] can be explain in a similar way as above.
The very common [soː] is consistent with *su.
To conclude, the Jamtlandic spelling for the
adverb 'so' is su.
Note that I am not 100% confident with su. It's possible (though unlikely) we must go back to an older etymology svo to base our spelling on. But until any new information on the matter is brought up to the surface, we'll stick with su.