Mark, these photos are so helpful. Thank you!
As I’m looking at them, I do wonder about one issue, and you may already have thought of it. When your oven is working, and afterwards, you are going to have hot flames and embers to deal with. I don’t think it’s going to be a big issue with the pergola (which looks really low, but I’m sure that’s more to do with the camera than the design), especially if you are using a chimney with a spark arrestor.
But you will need to protect your decking in the area immediately around the front and sides of the oven. Most ovens are built away from the house, and are surrounded with turf, dirt, gravel, concrete, or similar materials that aren’t subject to heat and flame damage.
Your oven intrudes into the deck area itself, so the mouth of the oven is about four feet above the planks. I’m wondering how you plan to keep stray glowing embers off those surfaces. Like I said, I’m sure you’ve got a plan, and it would help others.
My question is not strictly academic. My next door neighbors had a nice deck that include a covered pavilion where their smoker lived. One summer late evening we smelled smoke and looked out at about the same time a passer-by noticed the same thing. The neighbors had their house closed up and the A/C running, so it took the fire department arriving to finally get them out back. Glowing embers from the smoker had dropped through a vent and onto the wooden planks, and yes, they were just about to flare. Since the deck was attached to the house, the house would have been next, and the neighbors wouldn’t have known until their kitchen was on fire and the smoke alarms went off.