I just went to FedEx.com and rated from Los Angeles to New York. The only rate that came close to $16 was a FedEx medium box using one rate pricing. So I guess it depends on what you mean by "across the entire US". XL box was $31.36 using standard rate. The dimensions you listed would round to 12x11x11. All non-fedex packaging gets dim weight. FedEx packaging may or may not. That's why you can sometimes see a large variances for a similar sized box. What would happen if you select FedEx box but use your own packaging? You might get away with it or you might not. Which reminds me, I had a customer complain that when she dropped off at the location where I worked she got billed one charge. When she dropped at another location, she's got charged less and wanted to know why we were over charging her. We showed her how we rated her shipment and figured out the other location wasn't doing the dim weight and was under charging her. We told her we would correct the other location. 😁 Marking residential helps you get a more accurate rate upfront among other things. Also Express saver rates didn't disappear when I rated the FedEx boxes. More on reddit.com

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Fedex office stores can custom make a box but that costs a pretty penny. Uhaul or uline stores normally carry large boxes too. More on reddit.com