How would you make this joint ??

The most challenging part of this project is the fact that the legs are curved and offer no horizontal / vertical reference plane. I ended up building a square frame to mount them on to establish a horizontal / vertical reference plane to work off of.

I'm kinda stumped as to how to make the connection of the shelves to the sides (legs). There is a good glue area (2" x 2") but I'm afraid I need some sort of mechanical joint to resist load and racking. Normally a simple screw would do the trick, but in this case it would be difficult to hide the screw due to the multi wood lamination (I don't want walnut in maple or visa versa). I'm thinking of a half lap joint (see sketch) but would prefer not to embed the side rail into the frame.

How would you make the joint ?? Any and all suggestions are welcome, and if you have a better design idea, please speak up.

Pic 1 is my design I'm working from
Pic 2 is a sketch of the joint in question and the possible half lap joint
pic 3 is a the side rails showing the laminations -- I plan to trim the front of the shelf flush with the leg curvature.
pic 4 is the actual joint in question

Thanks, Tony

How about a dowl or a loose tenion ?

You mentioned glue area so I assume you're talking about a permanent joint and not something you can take apart and re-assemble. What about gluing plus countersinking a couple of screws inside the dado and into the legs. Then add glue in the dados and assemble both sides together as you slip the shelves into dados?

Couldn't you just screw through the center of the rail with short countersunk screws? the shelf would cover it, no?

Edit: oh nm. didnt fully read doug's answer...

:o :o I was so was so caught up with finding a COMPLICATED solution, it never dawned on me to simply hide the screws in the dado........ Thanks guys !!