Hmm, interesting idea and link for the sandwich board approach. In theory it would be nice just to breakout the signals needed on such a board, and it would make the board design easier. But I wonder if there is enough space in the case to accommodate more thickness. It might be possible, and only then require a thin copper shim to make contact with the case instead of the squidgy pad.
If this is not possible, then the it probably needs a new CM4 adapter board designed, with the required signals taken to new connectors on the opposite end to the gold fingers.