Try a CMaj7. Chords with natural 7s have a very mellow haunting sound that would fit this tune very well.
Decide on a Key. It will help to give some structure rather than guessing what will work and what won't.
You could go from a CMaj as a parallel minor in the Key of A, then go to an AMaj7 to a DMaj7 with an Emaj7/A for the turn around. At the end of the song go back to the Cmaj7 then resolve to The regular A chord for the finish.
The Amaj7 uses 3 fingers while the rest use 2 or one finger so it is pretty simple to play and it will sound good with any picking pattern.
Nothing above the fourth fret.
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