While you don't want continued leaf/plant damage, if you can wait 'til a nice cold snap comes along –one when the iguanas tend to fall out of the trees– then you could plan to police your area for the fallen of same said before the day warms up. (The smaller ones should be more susceptible to the cold.)
But eliminating them from your yard isn't a permanent soution but rather a stopgap one, because like with squirrels, nature abhors a vacuum and next season you'll surely have some new iguanas moving back into the now 'unclaimed territory' that you will have ccreated.
OK — HTH
Paul M.
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Thank you, that's a great idea and will hopefully work for at least a few. It's so thick up in some of these trees, they wouldn't fall all the way down unless perched on a lower branch. Going to try traps baited with papaya, mango, and hibiscus.
Have caught a few, when they get around the pool. The trick is to chase them into the pool. Then, follow them until they come up for air, and grab behind the head (and base of the tail) asap. Helps if you have something ready to put them in. Otherwise, you gotta an angry green clawed demon thrashing and whipping you, and no plan.