Your (Robert Price) idea is same as mine, however I think you need to either do it like Queens Left chess, or else allow bishops to not be colorbound.

I was wondering about pawns movement too like Bastien, but Gilman answered in a good way.

Using rules for shogi, since is 9x9 board (odd number of ranks), you need some way to know how to figure out the middle rank! One way could be, the middle rank is fixed and is always considered a part of the board. Using such a game with shogi also has a lot of other consequences: Rule of pawns movement mentioned in the paragraph above would also apply to nearly all pieces of a shogi game (王將 are the only exception). If you already have your own 歩兵 in one file, maybe you put together the boards that hide it so that you can drop another one anyways, and with boards rotated into place it can be caused even without dropping pieces into the board. Making a checkmate by placing 歩兵 into the board also is affected by which board is placed together.

With xiangqi, you can easily split the board according to the river, but then there is the condition of 將/帥 not being allowed to look at each other. Rules are required to consider this. For example, you can mean, you are not allowed to join together the boards which would cause such a condition, or you can use a 飛將 ("flying generals") rule, meaning you will take over the opponent's palace. The other thing is many name of pieces are different for each side, in xiangqi, such as 象 and 相. You can resolve this easily, by just picking one set of names, or just mixing them up whichever way you want.

It would be even more strange with Go. Again you need a fixed middle row. You could have multiple board pieces that can be joined together, although nobody owns one of them as opposed to another one. You can capture groups by picking which parts of boards to join, too. Rules about how you are allowed to lose your own pieces becomes more significant in this case. You could even play with three half boards but with only two players, even.