: If, on the other hand, we said, "tune 'em all in fourths", we would have E, A, D, G, C, F.
: Not too bad, but if we want to "come out even", we need a 3rd in there somewhere."

Why would you want this? The ud is often tuned in straight fourths (C# F# B e a d' in Turkish tuning, a tone lower in Arabic), so is the Puerto Rican cuatro (B, E A d g). Much more logical for reading melodies.