Because of physical condition of my left arm and hand including the thumb, to put the thumb on the back of the ukulele with even the slightest pressure would wet down my ukulele with tears. I use to do that with a 6 string but that was years ago.
What I am doing is playing Chord Melodies. Many of the songs have a melody note on string 1 fret 5 and call for the fingering 0235. So I am looking for alternate fingerings that I can use while playing the melody note on fret 5, string 1. I use mostly Mike Lynch books one thru three. The song I am working on now is an old favorite Irish number, Carrickfergus. I transposed it from an old song book, single note melody, to key of G so it would fit on the ukulele. In G I am still playing some notes on string 4. Maybe I could transpose it further up the fretboard, however, if possible, I would like to stay in G.