I am pretty confident in that not many would oppose the not so controversial idea to accept the combination hj- [j] even though the h is silent. For example, Old Norse hjorð [hɪ̯ɔrð] 'herd' has become Jamtlandic hjórð [juːɽ] where the h- is silent. This is how all North Germanic languages work, except Icelandic (pronounciation [ç]), to some extent in Faroese (both [j] and [tʃ] depending on word) and dialectally in "Bondska" (surpringly evolved into [he]).
It's also pretty obvious that the Old Norse combinations hl-, hn- and hr- (originally pronounced [xl], [xn] and [xr]), today preserved only in Icelandic (simplified to the assimilations [l̥], [n̥] and [r̥]), must be written l-, n- and r- in Jamtlandic. For example, ON hlíta [xliːtɑ] 'trust', acc. hnefa [xneβɑ] 'fist' and hrœra [xrøːrɑ] 'move, stir' have become Jamtlandic líte [liː.it], næva [næʋɐ] and røre [ɾøː.øɾ], respectively.
The interesting case that is left is hv-, in Old Norse pronounced [xw] (or, equivalently, [xu̯]). In Jamtlandic this first got simplified to [w̥], then to [w]. Note that at the stage when hv- was pronounced [w], v- was probably pronounced [ʋ] (in Old Norse [w], i.e., [u̯], without th [x] element). In fact, in 1791, Fale Burman (1758-1809) wrote in his Jamtlandic dictionary project:
1. gv, för att uttrycka orden hvila, hvass (acutus)
etc., hvilkas första consonant har sama uttal,
som wh i Engelskan.
This means that at least up until the early 19th century, hv- and v- were pronounced [w̥]/[w] and [ʋ], respectively. (I am not sure exactly how he thought English wh- was pronounced, but definitely not as [ʋ]/[v] which is the important thing.)
Apart from this modern historical fact, in northern Jämtland there's a North Trøndish dialect where ON hv- today is pronounced [kʋ]. (Perhaps not a very relevant fact, though.)
The observations above and the fact that Bokmål and Danish have hv- [ʋ], suggests that in Jamtlandic we should use hv- for historical hv-. For example, ON hvessa [xwesːɑ] 'sharpen' is in Jamtlandic hvesse [ʋɛ.ɛsː] (early 19th century: [w̥ɛ.ɛsː]/[wɛ.ɛsː]).
We conclude that we employ the
spelling hv- for historical hv-.
An important exception to the rule above is the case when ON hv- has turned into Jamtlandic [h], mainly in the ON combination hva-. For example, ON hvat [xwɑt] 'what' has become common Jamtlandic [hɔtː], so we spell it hut. (Note the choice of the vowel u, which happens to be the correct one to be consistent with all dialects.) This development probably suggests that between [xw] and [w̥] there was an intermediate stage [hw]/[hu̯]. This would give the following assumed development for ON hvat → J. hut:
hvat ~ [xwɑt] → [hu̯ɑt] → [hu̯ot] → [hʊt] → [hɔtː] ~ hut
We have assumed here that v was lost in Middle Jamtlandic, i.e., Jamtlandic as spoken in the period 1350-1500. (NB: Another common Jamtlandic word for 'what' is hvuð [ʋoː]/[ʋɔ], probably a developed from an old unstressed version of hut.)