The "Kind Friends and Companions" song was sung regularly by the late Sheila Stewart (of the Stewarts of Blair) and that'll be very likely where Siobhan and Jeana got it from. (Jeana is Orcadian too). Same tune as "Puir Rovin' Lassie" and a number of other songs.
The tune Kris Drever sings there is almost an inversion of the "Kind Friends" one: it certainly fits the same meter. On the YouTube it mentions Charlie McKerron in the credits: possibly he wrote the tune, as it says MCPS after his name? He is the fiddler with Capercaillie and other bands and has written plenty of good tunes.
By the way, I do also love Sir Peter Maxwell Davies' tune but it bears not even a passing resemblance to the one in Kris's song.