The Revivalists’ David Shaw was having an eventful weekend when we connected by phone on the 5th of July: He was in Chicago, about to participate in a superjam (with Soulive’s Eric Krasno, ex-Allmans bassist Oteil Burbridge, and others) for one of the many satellite shows around the Grateful Dead’s finale.

Orbiting the Dead put Shaw in touch with his formative musical experience—one-third of it, a...