I had a think about what it is I don't like about some of the complex arrangements of this song I've heard.

Look at the notes in it. It's hexatonic - no F. That's a fairly common mode in Scottish music, ambiguous between lydian and major. But the chords in that anonymous arrangement include the out-of-mode F almost all the time and obscure what's going on melodically. You don't always need to avoid out-of-mode notes, but with a simple but subtle tune telling a simple story, they don't help.

How would it work if you restricted yourself to C, G, and Am, and only let the accompaniment emphasise beats that correspond to emphases in the text (i.e. beats 1 and 3)?