I'm trying to find the cast of the touring company of "A Soldier's Play."
An interesting question. I'm afraid the question might be, are you sure there was just a single touring company?
The Negro Ensemble Company did a production—the main one, back in the early 1980s. Denzel Washington was part of that cast. Adolf Caesar was as well.
I'd research the Negro Ensemble Company (http://www.negroensemblecompany.org/), or contact them directly. They certainly would be able to list all case members.