Chess with Sudoku limitations
I don't have an exact answer for you here. Like any game in development you should test and iterate through different ideas in the search for the best one.

I'd come up with a solution you think is suitable, then go and play that game a few times. Does anything feel overpowered or wrong, then change it. You repeat this process until you get an ideal solution to the sitation.

Also well done for coming up with a really unique take on chess. For a game over 1000 years old it hasn't changed much since its origins, so it's impressive to see an honestly interesting take on a game that has such a well set up structure.