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This is an interesting notation system and should certainly be one that can be used.  In fact, if we had grown up using it it would seem very natural.

It reminded me instantly of one used by the Chinese for their Chess.  In that notation we find 3 important  directional symbols meaning: Forward, Backward, Horizontal (sideways).  So, if adopting the Chinese system we would see in the example game, instead of: 

1. P5 - n2    P5 - s2   (north 2; south 2)

1. P5 - f2    P5 - f2   (forward 2;  forward 2) [Direction is in relation to a player's first rank]

When the sideways symbol is used, then a number (for the file) accompanies it.  Thus we could see R - s2 (But be careful - because here it would mean sideways to file 2, not sideways 2 spaces.  Traditional Chinese files use numbers instead of letter designations.  

The Chinese also have symbols for the Back-most and Forward-most piece.  These are used when, for example, you have two White Rooks on the same file and need to identify which one is moving (the forward or aft piece).

When it comes to pre-sets Algebraic notation seems ideal.  Having each square (or hexagon, etc) labeled appears best to avoid confusion.  If we see e2-e4 we have no doubt as to a piece is moving from point A to point B.
When playing over Chinese games I do very well with their system [even though it is written in Chinese], but it did take me several games to have the system down well.  I expect it would be the same with this new Geographical Chess Notation.  Good job Abdul-Rahman.