Quite a number of years ago I ran across a Mel Bay instruction book on playing melody out of simple "pure" chords - ie. three string (or sometimes four string) chords on the highest three strings of the guitar, high E, B, and G. I don't have the book anymore, so I don't know the correct title. It was an eye-opener for me.

The moveable chord shapes were the 1st postion "D", the first position "F", a modified "A", "Dm", "Bm", etc. Just taking those shapes and sliding them up and down for melody and inversions can really open up the neck.

If you're fingerpicking one of those inversions usually throws the needed melody note up on the top string.
And, if you're in the right key (G or D?), you can still sometimes use the open bottom strings for your alternating bass without too much dissonance.