The bishops are limited to half the board so only need 5 bits for position. This frees up 4 bits, but you lose the capture state (can't use King's position for capture state). Well, you CAN use the king's position for capture state for two of the bishops at any given time. Then for the other two bishops use a bit to store their capture state. This saves 2 bits overall, bringing the total down to exactly 26 bytes.
Gonna have to think that through for awhile, not sure if it works out.
Update: I see a comment below that does this but uses 21 bits (instead of 22) by storing bishop position and capture state as a base-33 number.
The bishops are limited to half the board so only need 5 bits for position. This frees up 4 bits, but you lose the capture state (can't use King's position for capture state). Well, you CAN use the king's position for capture state for two of the bishops at any given time. Then for the other two bishops use a bit to store their capture state. This saves 2 bits overall, bringing the total down to exactly 26 bytes.
Gonna have to think that through for awhile, not sure if it works out.
Update: I see a comment below that does this but uses 21 bits (instead of 22) by storing bishop position and capture state as a base-33 number.