I agree that the way the bishop can change its square color through the singularity is inconsistent, as it actually should go in the reverse direction.
There can be interesting variations on the subject, some of which you just described. The simplest one can be to cut the board in half vertically, and then join it again by its borders. As a result, there will be no full U-turns, and the bishop will have five directions of movement in the board's central part, like in usual three-player chess made of three 4x8 board parts, which share somewhat similar geometry.
As a minor observation, it can be pointed out that this variant has natural reverse symmetry, so the black king and queen should switch their places to preserve their initial square colors. It also can be noted that the a and h pawns can capture each other from the initial position, so, there must be an artificial restriction to stop them from that.
I agree that the way the bishop can change its square color through the singularity is inconsistent, as it actually should go in the reverse direction. There can be interesting variations on the subject, some of which you just described. The simplest one can be to cut the board in half vertically, and then join it again by its borders. As a result, there will be no full U-turns, and the bishop will have five directions of movement in the board's central part, like in usual three-player chess made of three 4x8 board parts, which share somewhat similar geometry.
As a minor observation, it can be pointed out that this variant has natural reverse symmetry, so the black king and queen should switch their places to preserve their initial square colors. It also can be noted that the a and h pawns can capture each other from the initial position, so, there must be an artificial restriction to stop them from that.