I wrote out the scales of each of the modes, then added a 3rd and a 5th on top of each scale step (using only notes of the mode) to see what kind of chord sequences I got

Don's methodology as used by 19th century Scottish musicians: the duets from my Old Scottish Flute Music collection, except that they used a 3rd, 4th or 5th below.

Probably they got the idea from hymnbooks. Works fine for two flutes, but the chords change way too fast for a voice and guitar arrangement, it would sound frantic. I guess Don simplified the accompaniment lines that his procedure suggested. (The Tunes with a Bass part of my collection is a lot more sophisticated and uses no simple rule-based procedures - it's more like what a good guitarist would come up with).