UPDATE: I was contacted by reps from BBQ Island to resolve my issue with the spurious credit card charge. When I called they knew my situation by name and refunded the charge immediately. The rep offered sincere apologies for the mix-up. It appears the temporary help hired to work the Sportsman's expo never filed the paper invoice. So there was no record of my order outside of the remote credit card machine. I was impressed with how serious they took the problem. They asked me what they could do to make it right. I had already purchased a Yeti Cooler from another vendor months back so they graciously sent me a gift certificate.
I was won over by their prompt and sincere efforts to make the situation right and believe the mistake was innocent and largerly beyond the control of the full time staff.