Mr. Clicker, you are right, but that is no fun.
I tried playing with a simulation last night. I think this will work. If the fingers are not long enough to bottom out on the opposing side. It will leave small openings but these are no good for holding glue anyway as they are endgrain, and will not show. It should be a strong and self aligning joint, but does not get to show off anything. Only you will know what is inside the joint.
Two pics, one of each side.
Steve