Joe Iconis spent years writing “The Untitled Unauthorized Hunter S. Thompson Musical,” before finally being invited to walk in the famed journalist’s footsteps.

Hunter S. Thompson grew up on Ransdell Avenue in the Highlands neighborhood. An incident in Cherokee Park sent him in a different direction, one that would influence his life.

Two shows on stages just outside Washington, “ The Untitled Unauthorized Hunter S. Thompson Musical ” and “ John Wilkes Booth: One Night Only!,” create a diptych of American mythmaking ...