Here's Healy's tune. After all my work in identifying it, I find the 2nd tune below on the same page, only a slight variant.

X:1
T:LOVELY BANNA STRAND
N:Healy's Irish Ballads and Songs of the Sea
L:1/8
M:6/8
K:D mixolydian
F/2G/2|A2dd2B|c2B AG E|A2ED2 D|(D3D)z A|\
D2EG2A|d2ce2d|c2A BA G|(A3A)z A|D2EG2A|\
d2ce2d|c2A BA G|(A3A)z (F/2G/2)|A2dd2B|\
c2B AG E|G2ED2D|D4|]

X:2
T:Van Dieman's Land
N:Healy's Irish Ballads and Songs of the Sea
L:1/8
M:6/8
K:D dorian
(F/2G/2)|A2dd2B|c2B AGE|(G2E)D2D|(D3D2)D|D2EG2A|\
{A/2}d2ce2 d/2d/2|c2A BAG|(A3A2)G/2E/2|D2EG2A|\
(d2c) e2d|(c2A) BAG|(A3A2) F/2G/2|A2d d>cB|\
c2B A>GE|A2ED2D|(D3D2)|]

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