I think you would be better served by using the aluminum cleat hardware (inner & outer cleats) & an outrigger leg, which can telescope a bit. It's a compromise I know, but it would be light, strong & easy to set up on uneven terrain. We have small shelves at our galley, but your BBQ needs to be far enough away from the sides & supported well for weight. A cantilevered shelf would need to be strong & well attached to work, but it's starting to look like a fair amount of engineering to make it work properly. I still like the KISS method for everyday use.
This is what we did for extra space, but there's not much of a load & the shelves are relatively small. Aluminum extrusions & folding supports work well enough for light stuff.



In the bottom shot, the rearmost support was 'blocked out" with a small cleat, which was attached to the 1/8" interior side prior to skinning the outside. The folding supports have padded edges (bar top non-skid glued in place), so the painted aluminum won't scratch when the shelves are set in place & carrying weight.