Jack as you suspected the tunefinder tunes look like the ones from the DT:

King Orfeo Song Entry, with tunes: King Orfeo - Kity Anderson's tune midi and King Orfeo - John Stickle's tune midi. (Note that the lyrics given in the DT are not for either of the versions with tunes; John Stickle's lyrics are posted above and in the other thread I linked above. I'll try and get round to posting Kitty Anderson's version later - it's not dissimilar to the Child version in the DT). The tunes are substantially as given in Bronson, though in Bronson John Stickle's tune also gives a slightly different version for the 1st line of the last verse.

Here's the full abc for both, with the lyrics. Bronson doesn't give aligned lyrics (except for that 5/4 line), so I've guessed in a few places on the scansion. (I do have the John Stickle recording on the old Topic Child Ballads record (vol4) and I could dig that out to check if anyone's worried about that. I don't have the Kitty Anderson version). (I'm also in a bit of a rush, so I haven't bothered too much about the exact modes in the abc.)

Mick

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X:1
T:King Orfeo
B:Bronson: The Singing Tradition of Child's Popular Ballads
C: Sung by John Stickle, Baltasound, Unst Apr28 1947
S: Collected Shuldham-Shaw
L:1/8
M:4/4
K:Gdor % Bronson gives mode as P pi4 (P/Ae/D intersection)
"<("">)"F2|GFGB c<d c2|
w:* Will ye come in-to our Ha'
BG(FD) C3
w:Scow-an Earl_ grey
B,|B,B,BG (GF) (G/F)
w:Yes we'll come in-to your_ ha'_
D/|CB,CD F G3|]
w:For yet-ter kan-gra nor-la.
[M:5/4][L:1/8]"^Additional tune for last verse:"GF GB cd cd c2|
w:Then they played the good old gab-ber reel,
[M:4/4]BG(FD) C3||
w:Scow-an Earl_ grey

X:2
T:King Orfeo
B:Bronson: The Singing Tradition of Child's Popular Ballads
C: Sung by Kitty Anderson, Shetland
S: Collected Collinson, School of Scottish Studies, rec No. 1955/145/6
L:1/4
M:3/4
K:Ddor % Bronson give mode as a pi4 ending on V
D|D/A/ A>G|A/A/ A2
w:Der lived a king in-to da aist
[M:2/4][L:1/8](GF) DC|[M:3/4][L:1/4]D2
w:Scon_ner le groon
D|D/D/ d>d|c/A/ HA>
w:Der lived a la-dy in da wast
G|[M:2/4][L:1/8]FF DF|[M:3/4][L:1/4]G HA|]
w:What yor-ten han groon var-lee