Ahh I'm a singer who always hear (or even make up) the harmonies in songs and I now I sort of understand what's going on in my ear. And you've given me permission to go with the harmony that works and not worry whether it's the "right" one (esp when it's only two part). Thanks!
Very good! Correct me if I'm wrong. The single Bass note you're playing with your left hand determines the chord inversion regardless of the order of the upper notes. Also I assume that the top note in the right hand is the melody note, so the three notes in the right hand aren't always root position triads.
"How to harmonise a melody in a really, really boring way". Or… Oh, wait, wait a moment. Doesn't the Beethoven's Concerto No.5 open with the biggest… no, the BIGGEST EVER (my font is still too small) I-IV-V-I progression in all music? 🤔