Heya... The 'Summertime, Summertime It Will Come' tune on Chieftains 5 is a Paddy Maloney composition, which may (or may not) have been inspired by the tune "Eibhli Gheal Chiuin ni CHearbhaill" (Fair and Beautiful Eileen O'Carroll? Ask Frank Gallagher or another Gaelic speaker for translation!) on Chieftains 3, which is most definitely the tune used by the Steamshuttle band on their eponymous album to carry the (edited) text of 'Hump the Drum' whose only previous existence (as Guru Bob points out) was in a Ben Bowyang Songster. It's in Bill Scott's big book.
No possible relation to 'Star of the County Down'. Different mode entirely.
Nice version but! There are more words in the original, though the WW1 bit is NOT there, an interpolation of that other Graham's I think.

Cheers from 40 degrees South... Branno