Please reconsider your approach, you seem like a very nice person, but you are having one heck of a bad approach.
For instance, you said you want to make what you already have done work, it does work for a reason. Wrong type branches. Well, as far as I know, you can make large branches smaller, but you cannot make small branches larger. I guess you can make smooth branches rougher, but it surely would be easier to just get new ones.
The bad approach part is(in my opinion) your confusing problems. Your kids getting poison oak, is not a problem to be confused with getting branches and limbs. Teach your kids what posion oak is, that is seperate from getting branches. Teach them to avoid the poison oak. IF they find a beautiful perfect branch in that stuff, then teach them to send one of their friends after it, hahahahahahahahaha(many ways to skin a cat)
The problem and joy of monitors is, they keep you looking for those many ways to skin the cat(poor cat) Remember, putting a free ranging active reptile into a small cage(any cage, not yours) is already a magic act all by itself. So your main task is the ability to adapt and be creative, not use what you have already tried.
I would not say any of this to you if you were a normal petshop repta tankola person. But you have already shown that you are willing to put lots of effort into keeping your monitor.
The truth about keeping monitors, is the effort never stops. Again for instance, if what you do works well, then your monitor grows like a weed and you have to change the cage furniture, then the cage. If it does't, then that is a disservice to the monitor. See what I mean?
I believe your first error was in the choice of species. You should have picked a species that only gets the size your monitor is now. Not pic a monitor and build a cage for it, just to find out, if you do a good job, it will outgrow the cage very quickly. Consider, if you do a bad job, the monitor outgrowing the cage will not be a problem. But from the looks of the cage, you like to do a good job. Good Luck FR