I used to play some Leadbelly. I learned by tuning my guitar to his and playing along. I found his guitar was usually tuned down about two full steps, so that a fingered "E" chord was actually a "C" chord in pitch. Regular strings weren't heavy enough to carry the lower tuning. I found LaBella "Heavy Gauge" strings worked well, though they required building up your finger strength some. I no longer have a 12-string and have no idea whether LaBella Heavy Gauge strings are still available. Fannin Street was in (fingered) E, John Henry was in D, Silver City Bound was in D, and son forth. He had a very active thumb; most of the power of his playing was thumb strokes. I think he did use picks, at least I'm pretty sure I recall a picture that showed picks. I sure had to use them to reproduce what he did. Didn't know Cooney played Leadbelly. I saw him in concert in the late 60s. He played six string and banjo.