There are some considerations that might help the discussion – music notation is an abstraction, whereas tablature is more of a ‘practical’ mapping of notes to just one kind of instrument. Notation conveys far more than just “where does my next finger go” – it’s interpreted by singers, guitarists, pianists, drummers, whomever – it’s universal and cross-platform. Actually, if you look at any midi sequencer you’ll see alternative representations of music as data, similar in concept to the proposal above, though typically oriented west-east rather than north- south. Pitch differences appear ‘higher’ or ‘lower’ which maps better to the physical sound experience than ‘left’ or ‘right’ (which also has no parallel for e.g. horns or string instrument).
Look at Cubase or Logic for existing display methods, it may inspire your v2.