In Swedish dialects and folk traditions 2004 (ed. Maj Reinhammar) in the contribution En jämtländsk 1700-talsdikt by Maj Reinhammar where a mid 18th century Jamtlandic (presumably in the Offerdal dialect) poem is analyzed, it is written
Jämtskans öppna »grumliga» ö-ljud, som fonetiskt
brukar tecknas med »åttan» (stundom å-haltigt) eller
»skålpundsåttan» (u-haltigt) skrivs i dikten med ö,
t.ex. nöna 'nu', (3 o. 21), hör (44 o. 47), döm (19),
söm (20; vanligen såm 16, 21, 27 o. 34), nör (16),
örskje (12), körskjen (26), föll38 (29, 35 o. 41),
-örta (36), [...]
(The numbers within parantheses refer to the line in the poem.) The sounds in question are what in IPA are written [ɞ] (»åttan», i.e. "the eight", in Swedish Landsmålsalfabetet, i.e. 'The Dialect Alphabet') and [ə̹ ] (»skålpundsåttan», i.e. "the pound eight"), where the latter is a rounded schwa.
Fig. 1: Swedish Landsmålsalfabetet. (Source: SOFI.)
The two interesting words in the context are örskje [ˈɞʂːə] 'wood, material' and körskjen [ˈtʃɞʂːən] dat. 'the church', derived from Old Norse yrki [ˈʏrcɪ] and kyrkju·nni [ˈcʏrcɪ̯ʊnːɪ], respectively. Note that the spellings are semi-etymological in that the k is spelled out, one would've expected rs rather than rskj to denote [ʂː]. It can't be ruled out that rskj denotes an earlier stage in the phonetical evolution, perhaps [ʂtʃ].
Let's take a look at what these too words are in Hammerdal dialect (H), Klövsjö dialect (K) and Åre dialect (Å), where we employ the usual references:
H K Å
yrki [ˈœ.œʂː] [ˈœʂːə] [ˈœ.œʂː]
kyrkju [ˈtʃœ.œʂː] [ˈtʃœʂːə] [ˈtʃœ.œʂː]
(Note that I have considered ON kyrkju rather than kyrkju·nni.) We see that all dialects in question have developed yrkj into [œʂː]. Does this mean we should spell yrkj, as according to the etymological spelling? (Compare with e.g. kyn [ tʃøːn] 'gender', ON kyn.) Or more phonetical as ørkj? There's another choice, namely orkj. This seems suggestively more consistent with [ɞʂː] of mid 18th century Offerdal dialect, and, in fact, more consistent with what has happened to ON yrk.
To explain what I mean, consider the more general situation of ON yrC and yłC where C denotes an appropriate consonant, e.g. k. To be specific, consider e.g. ON myrk- 'dark', kyłd n. 'cold', and fylgði imp. 'followed':
H K Å
myrk- [mar̥k] ? [mɔʂk]
kyłd [tʃaɖː] ? [tʃɔɖː]
fylgði [ˈfa.aɖː] [ˈfɞɖːə] [ˈfɔ.ɔɖː]
These samples are perfectly consistent with the spellings mork, kjołd and fołde with o rather than u (or á, or any other vowel) as a stem vowel. Adding a j in the equation, one would get suggestively an implied i-umlaut of o. This would give the spellings orkje 'wood, material' and kjorkje 'church'. It's the j which tells us that o is pronounced as if it were spelled ø. One could imagine the spelling ø too, i.e., "ørkje" and "kørkje", respectively. This could need more discussion.
To conclude, ON yrkj is spelled orkj, though it
can be in principle ørkj as well.
Next time I'll probably discuss the second person plural verb ending -in found in the word vilin [ˈʋɪˑlɪn] 'want' in the poem discussed in Swedish dialects and folk traditions 2004.