Knowing what I know of playa shade/cooling, you'd want to have at least a foot on each side and above between the tent and the shade. The sun hit's the shade material and radiates heat in all directions. Based on that, a 10x20 carport wouldn't be big enough just based on the sides. If it's tall enough for the tent, you might want to consider rigging two carports together (to get 20x20), or look at a conduit frame structure.
Could you angle the carport so it's facing north and have the tent extrude for a foot on that side? Or even stick a couple of poles so that the side isn't touching?
The Lady with a Lamprey
"The powerful are exploiting people, art and ideas, and this leads to us plebes debating how to best ration ice.
Man, no wonder they always win....." Lonesomebri
I think the Kodiak will work fine in your 10x20 carport if you replace the side poly tarps with shade mesh tarps. I added a 10x20 silver tarp under the original canopy cover, and that helps keep the heat from soaking through the top. I do like the idea of two carports connected together for a shaded hang out area in front to the tent.