Step 1: Mod SNES casing - preparation stage
Remove the parts of the casing highlighted in green on the pic with the controller front opened up.
In the last picture, it shows the areas you need to trim off the case backing so the BGP100 board will bit in place.
Step 2: Trim the SNES board down a bit
Step 3: Remove the BGP100 controller board
The board section with the D-pad can be removed as it is only a contact board that uses the wires to connect to the button presses. The board with the chips on it is the proper controller board.
The D-pad and left shoulder button use a common grounding, however the right shoulder button and the other buttons do not use a common ground, so you need to wire both sets of contacts per button to the SNES board, and keep their contacts unique.