I think it'd be a good idea to take a concrete example from Vidar Reinhammar's contribution in Jämten 1987 (see this post). In the beginning of his contribution he discusses how Old Norse u [ʊ] today is pronounced in the Jamtlandic dialects. Supporting the idea a unified Jamtlandic is possible, I'll try to do my best to meet his examples. He writes (translated by me from Swedish to English, the red information being added by me for clarity):
"Old short u (Old Norse [ʊ]) appears in the Jamtlandic
dialects in most situations as u [ɵ], å [ɔ] or ô [ɞ] (i.e., a
sound between u [ɵ] and ö [ɶ]). Swedish hund [hɵnd]
('dog', ON acc. hund [hʊnd]) is pronounced in all of
Jämtland hunn [hɵnː], but Swedish mun [mɵnː]
('mouth', ON acc. munn [mʊnː]) is pronounced in
Alanäs, Ström, Hammerdal and Gåxsjö mônn [mɞnː],
in Lit, Häggenås, Laxsjö, Föllinge and Hotagen månn
[mɔnː] and in other Jamtlandic dialects munn [mɵnː].
The Swedish rhyme word tunn [tʰɵnː] ('thin', ON þunn-
[θʊnː]) is pronounced tunn [tʰɵnː] in Åre, Undersåker
and Kall and the Norwegian Lid dialect in Frostviken,
but tônn [tʰɞnː] in Lower Frostviken, Alanäs, Ström,
Hammerdal and Gåxsjö, Borgvattnet, Stugun, Ragunda,
Håsjö, Hällesjö, Nyhem, Bräcke, Bodsjö, Revsund,
Sundsjö (also tånn [tʰɔnː]) and Berg, and in other
Jamtlandic dialects as tånn [tʰɔnː]. If we consider
Swedish rund [ɾɵnd] ('round', ON rund- [rʊnd]) rhyming
with hund [hɵnd], it has like tunn [tʰɵnː] the
pronounciations runn [ɾɵnː], rônn [ɾɞnː] and rånn [ɾɔnː].
Thus, there's no uniformity in how Swedish u [ɵ] is
pronounced in the rhyming words mun [mɵnː], tunn
[tʰɵnː] and hund [hɵnd], rund [ɾɵnd], respectively."
Now, let's refute his argumentation. His argumentation is that except for how Swedish hund is pronounced, the dialects disagree on the choice between the possible [ɵ], [ɞ] and [ɔ]. Therefore, there's no way to employ a unified spelling for the words in question. I guess he also argue that the geographical distribution of [ɵ], [ɞ] and [ɔ] isn't even completely predictable when given a word whicb in Swedish (and Old Norse) has u.
The first issue is easily refuted by using the etymological principle. One could simply spell the words húnn, munn, tunn and runn. Note that short ú is always [ɵ] no matter the dialect. The second issue is more serious since given a dialect we don't know from the orthography only how munn, tunn and runn are supposed to be pronounced. This is solved by the following argumentation. It's obvious that there seem to be one geographical epicentre for each one of the possibilities [ɵ], [ɞ] and [ɔ]. In Western Jämtland one has an epicentre [ɵ], in Northeastern Jämtland one for [ɞ], and in Central Jämtland for [ɔ]. The exact distributions for every word varies, but the epicentres are always fixed. This suggests that the words individually have dissipated into "foreign" areas through not so well-defined boundaries. This means that the only dialects we sacrifice when fixing the spellings munn, tunn and runn are the boundary ones. For Jamtlandic as a whole, we can safely employ unified spellings. In "polished" Jamtlandic, one can choose a consistent way of pronouncing a short u, one just chosse one of the epicentres.
To conclude, we write húnn, munn, tunn and runn.
It's possible I'll return to other concrete examples which Reinhammar discusses in his contribution. I think they can all be solved in a similar way. In some cases one would probably have to defined what's the "best" (i.e., most genuine and/or distinctive) Jamtlandic.