Here's my deduction of who played whom in Dr. Talos's play, based on explicit statements, physical characteristics, and the constraint that no actor can appear in more than one role simultaneously. I'm sure many readers of this list have already worked this out, but others may welcome it as a useful reference for the present discussion. I will gladly receive additions and corrections.
-- Dan Rabin
Gabriel - Dr. Talos
The Giant Nod - Baldanders
Meschia, the First Man - Severian
Meschiane, the First Woman - Dorcas
Jahi - Jolenta
The Autarch - Dr. Talos
The Contessa - Jolenta
Her Maid - Dorcas
Two Soldiers - Dr. Talos and Severian [note 1]
A Statue - Baldanders
A Prophet - Severian
The Generalissimo - Severian
Two Demons (disguised) - Severian and Dorcas
The Inquisitor - Dr. Talos
His Familiar - Severian
Angelic Beings [note 2]
The New Sun
The Old Sun
The Moon
[note 1] Dr. Talos must be First Soldier and Severian Second Soldier, because First Soldier and Familiar appear together in a scene. Also, Second Soldier's role requires physical strength (carrying Jahi/Jolenta), which we know Dr. Talos does not possess (see The Sword of the Lictor).
[note 2] I don't think it obvious who plays which demon. Both demons
appear simultaneously with Autarch/Talos, and Second Demon appears simultaneously with Nod/Baldanders and Jahi/Jolenta. The pair must thus be Severian and Dorcas, but which is which? I favor Severian as Second Demon because 1) his prophecies in the first demon-scene include the line about natural resources cited in an Epilogue by Wolfe, and 2) Second Demon adopts the stance of a soldier (one of Severian's roles) in the second demon-scene.