Thanks Jorge for pointing me to the page with the discussion of chess with different pawns. This article has gotten me to thinking about the play balance dynamics of Spartan Chess.
Spartan Chess uses a slightly modified version of a berolina pawn for the hoplites which do get stronger as the game goes on and as the board clears; just what the article points out. Spartan Chess stays balanced because as the hoplites get stronger the Persian pieces also get stronger than the Spartan pieces, on average. Their bishops and rooks are definitely stronger as the board clears and they can exercise their full power on long clear diagonals and files.
I would share the complex calculus and ground-breaking mathematical calculations that went into balancing the game given these two off-setting dynamics but I cannot since there is none.
But seriously, having read the article and having time to reflect on the asymmetric play-balance dynamics of Spartan Chess I am delightfully surprised that it has worked out.