>With a 5/8 in. rabbet the standard depth for a deep is 9 19/32 . . .
Not true. The rabbet has nothing to do w/ the depth of the box.
A 9-1/8" frame will fit inside a 9-1/2" box if the rabbet is 3/8" deep or 3/4" deep.
The rabbet determines where the 3/8" beespace is located.
If the rabbet is 5/8" and box depth is 9-1/2", there will be 1/4" beespace at the top and 1/8" at the bottom. Once the boxes are stacked, there will be 3/8" between the frames and a 1/4" beespace under inner cover. The 1/8" space at the bottom of the stack will add the the 7/8" of a standard bottom board to make 1" from the frames to BB (thats "standard" too

).
Frames come in many sizes close to 9-1/8". Get your frames FIRST and make the box 3/8" taller.