How do I do this?

[EddyCurrent]

Taking into account what you said, maybe this idea would be easier. Laminate three pieces for each part, I've coloured the wood differently so you can see the laminations easier. You could leave the ends square or mitre the outside ones like the example. Use Titebond Original glue. Provided the pieces are all planed to the same thickness you should have a perfect fitting joint.

The one in your picture is called a "corner bridle joint".
The one in my picture is a "mitred corner bridle joint".