Oh my, we missed your post entirely in all the excitement over the hurricane, Diane.
I'm very glad we don't seem to have any iguanas here . . at least not yet, that I've heard. But from what I've seen in the Caribbean where they seem to be everywhere, they are good climbers so I don't think vertical gardening is going to necessarily help you unless you can put a pot on top of a steel pole, and then grease the pole so they can't climb it.
The lady I know in Grand Cayman grows her veggies in cages. She just made light, cheap cages out of PVC and chicken wire, and she pegs them into the ground with tent pegs so the iguanas can't get under them. They need to be enclosed all around and over top because the iguanas will climb the wire to get at the tomatoes and your other goodies.
