Richard Tarleton died in 1587 or 1588, and didn't really overlap Shakespeare. Will Kemp was succeeded by Robert Armin in 1604. There's a version of "Go from my Window" in Tho. Dekker's 'The Rape of Lucrece'. By and large the tunes by Dowland, Morley, Jones, Campion, et al. weren't in ballad and folksong style. Most of the original songs for the tunes in 'The Beggars Opera', 1728, are known (see the Ballad Opera Tune Index on my website).