I'm glad to see that you are at it again. I've also got the itch to make some patio chairs of similar design but do not really know where to start. I will be following along for inspiration.
BTW, I see that you are using Vcarve for your CNC. Have you tried using the tiling feature for machining pieces too large for your machine. I've used it a few times by sliding the pieces through the Y axis. That might allow you to machine the long sections from a single piece of material rather than having to join them. The key is creating a means to slide the piece precisely between tiled sections. I usually machine alignment holes in my CNC spoil board or a fixture that is clamped down to the bed and use corresponding alignment holes in the waste areas of the material.
--Nathan, TX. Hire the lazy man. He may not do as much work but that's because he will find a better way.