I had nothing extra covered with AAA on my TJ and it had even more on it than yours does. My TJ was stolen in March and they covered far more than they were obligated to, probably double what they were required to pay. I've heard of others having similar experiences with AAA. I'm not leaving AAA, I was treated more than fairly by them, they were amazing. They even hired an independent adjuster who knew Jeeps and he really helped. All I did was provide them a very detailed Excel spreadsheet with every item on it with links and prices paid, plus photos of most the items on my TJ with copies of as many receipts as I could find. That was enough for AAA to know my TJ wasn't the usual loss claim which prompted them to hire the independent claims adjuster who, again, really knew Jeeps and the brands of parts I had installed.
I still didn't get enough to fully cover my losses but I came out a LOT better off having had AAA than any other insurance company based on what the independent adjuster told me. He told me I would have been screwed with Progressive, State Farm, Geico, etc.. When AAA called me afterwards to ask how I felt the process went, I basically told them AAA has a customer for life. They really took care of me.
Something I did not know until after all this... AAA is a not-for-profit company, it is owned by us insureds. A mutual in other words.