I gather from the comments that my version is not easy to understand.
I don't know if it's that or if you just haven't explained it clearly.
But if I see it correctly, then there are no bugs in the variant and the set of rules is consistent.
With respect to the Bishop, you told me that it can occupy only 4 or a4 or only 5 or h5. I presume the same holds for other pieces. So, a Rook on one of these spaces would not command two files. Likewise, a Knight on one of these spaces could not move as though it were on the other space. However, that looks like what the Knight is doing in your example. It's on 5, and its ability to move to f4 or g3 makes sense in light of that. But its ability to move to e4, f6 and g7 would make sense only if it were on h5 instead of 5.
I don't know if it's that or if you just haven't explained it clearly.
With respect to the Bishop, you told me that it can occupy only 4 or a4 or only 5 or h5. I presume the same holds for other pieces. So, a Rook on one of these spaces would not command two files. Likewise, a Knight on one of these spaces could not move as though it were on the other space. However, that looks like what the Knight is doing in your example. It's on 5, and its ability to move to f4 or g3 makes sense in light of that. But its ability to move to e4, f6 and g7 would make sense only if it were on h5 instead of 5.