The idea of a circular board may yet be explored, if not here then for
another three-player game. I had some of the pieces in mind first, and
their use made a board without squares more trouble than it was worth.
In face-to-face play, White and Black tend to sit at their respective ends
with Red along a long side. It works. Also, in face-to-face we always
structured the board with a thirteenth 'rank' just like the picture.
Players freely swapped any piece on the 12th to either end as needed, to
help visualize the situation around the cylinder.
I'm glad you liked the game. The Shifting Alliances rule is one design
feature I'm particularly happy about.