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Okay, I'll put a preset together. Do you have any preferred piece icons, or shall I just do it, then we can discuss possible substitutions? [If we play our cards right, we just might suck someone in to playtest our 2 games in a compare and contrast mode, which might be some kind of record for this site. Have we ever had 2 higher-D games looked at together this way?] 

As for the notation, be careful! You've got me thinking... Seriously, the simpler the notation you can describe things in, the deeper the understanding you might get. [There's a branch of math where you start with 0, then the next number is the successor to zero: S0, and the next is the successor to the successor..., so that 3 is written SSS0.] As you might have imagined, I'll be happy to discuss notation with you, too. The problem with using an 'orthogonal prime' as a 'diagonal' in your game is that 'orthogonal prime' is not appropriate for that, in your game. W' is most logically a 3D wazir, not a 2D ferz. The way your pieces work, you want, for ease of handling, a way to look at 2D and 3D components of both orthogonal and diagonal moves. My notation is a compromise between your simple and unambiguous but directionless notation and something that only a math major could love.  

Now, in 3D Great Shatranj, the W' and D' notation are far more useful, because my 3D elephants are just 3D warmachines rotated in 2 of 3 dimensions, and have 'exactly' the same moves otherwise. Weak analogies to particle physics are noted, as the rotation of the 3D wazir splits it into 3 3D elephants, breaking symmetry... and now I gotta run. Enjoy.