The "o" above the chord indicates a harmonic as you've said. But I'm sure it means only the top note of the chord should ring out as a harmonic, not the whole chord.
I would finger the three (or so) notes of each chord with the left hand in the usual way, i.e. as the notes are written. Then when sounding the chords with the right hand, hold the index or middle finger lightly against the first string at its midpoint. Sound the notes together and lift the whole hand away as one action - you'll have a chord with one high octave chiming "above" it.
So your left hand will be playing chords as normal, the right hand will be plucking chords but with one finger reaching to around the 12-15th fret gently stopping the top string each time. (It is important to perform this without looking in any way flustered or distressed...)
This will be a demanding bit of technique. I've only used this in simpler ways by playing one bass or accompaniment line plus a melody line above it, picked out in harmonics. On the right hand the thumb plays the bass or accompaniment, the index finger stops melody note harmonics around the upper frets and the little/pinky finger plucks those harmonics nearer the bridge. (Think "Albatross".)