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I like this idea. I also invented game, where pieces moves as in all 3 games (sounds simple, but some rules are pretty complicated) and send it by e-mail, but it has not been published...
Wich further variants are possible?
Pieces can move only if move is legal in all 3 games: completely unplayable game!
Pawns moves 1 orthogonally forward, cannot capture, on last rank promotes to piece, wich moves and captures 1 sideways. King moves like in XQ, including palace and bare facing. Queen 1 diagonally forward, cannot leave palace (what a weak piece!). Bishop cannot move at all. Knight moves only in 2 forwardmost directions and like mao, cannot jump, don't promote. Rook moves only forward and again, don't promote. Right special piece moves as rook, but cannot capture. Left special piece don't move at all.
Not interesting! Variant, where pieces makes move, wich no of 3 games shares with 2 others is much more playable:
Pawns on first move can make non-capturing duoble step, can capture diagonally forward, on opponent's half of board can move and capture 1 sideways, on one of 3 last ranks (but not on latest!) promotes to queen, on last rank promotes to other pieces (wich are further promoteable) or stays unpromoted.
King cannot move expect for castling.
Queen can move as queen, but not as gold general, when in palace, can only move 1 diagonally backward to leave it.
Bishop can move diagonally, but at least 3 steps (can also move 2 steps diagonally to cross river), plus one orthogonally forward, on 3 last ranks promotes to queen.
Knight cannot move in it's 2 forwardmost directions, can go in other directions only if leaps over orthogonally-adjecent piece, promotes on 3 last ranks to queen.
Rook cannot move expect for castling.
Right special piece can capture as cannon, cannot move without capturing; after promotion can also move and capture 1 diagonally.
Left special piece can move as cannon and bishop, after promotion cannot move 1 orthogonally, but can capture.
Before i had idea, where half of pieces can move as in FIDE, but on as in XQ, other half can move as in FIDE, but not as in Shogi. Two kings. Four special pieces: 2 grasshoppers (considered as related to cannons), chanselor and archbishop (considered as related to flying chariot and angle mover). Probably, more playable.
Other ideas?

(posting with name only as I've lost my password. I haven't been involved
in chess variants for a while, though I would still like to do more with
them eventually)

Thanks, Daniil. I had had one other idea along these lines, which was to
combine all the modifications made to Shantranj to get each game. But I
found that in that system, it was possible for Black to force a win within
a few moves, so it wouldn't be a very good game at all.

And playing your game will join my long lists of things to do eventually.

one other thing I'd like to say since I don't know where to put it here
otherwise; the idea that large board variants are intrinsically unplayable
or unfun is plain wrong. I've played and enjoyed one many times, with
small pieces on a large board painted by my father, and I have played and
enjoyed other boardgames just on ruled-on paper so if necessary I think
poster paper or butcher's paper could be used for a board.