I actually had a very similar experience on my trip to South America flying Qantas and LAN. Traveling to anywhere in the America's as a silver and above FF member you are allowed 3 pieces of checked luggage at 20kg's a pop. I always have my carry on luggage (1 bag), and my camera bag. It's 2 pieces, but the camera bag is more like a laptop bag and it has never been a problem on the 20+ flights I've taken both bags on. That was until this Qantas flight through Auckland. When I was boarding the lady checking tickets said I had too much stuff and that I'd need to check a bag. I said OK no problem and she directed me to her manager. I had my check in bag receipt for the 2 bags I already checked and he proceeded to rudely tell me how I snuck my extra bags past the check in counter and how that was unacceptable. I explained that I am not a spy and didn't sneak anything past check in, and I asked what he was talking about. He said there is no way I had any business trying to carry on that much stuff. I explained to him that every time I fly to NZ this is exactly what I carry on and it is never a problem, and check in also had not problem with it (even though I did not ask them as this is the norm for me).
I then explained that I had no problem checking in my 3rd bag and asked that we get on with it. He said sure, that will be $150. I then said your own airlines rules state that I am allowed 3 checked bags. I broke out the IPAD and tried showing him on the website. He refused to look, said too bad, and also said that I can't board the plane unless I pay, or I can leave my bag. At this point I broke out my iphone, snapped a photo of him, and then I began to video record the conversation. In interview style I spoke his name and asked him why he was not following his own employers rules. He filibustered the question and said he did not care and I can leave my bag. I said the $150 fee he was attempting to extort was outrageous, and that I have never been treated in this manner by any Australian company, let alone Qantas. He then said that he can go get his manager and that the manager will charge me more that $150 and he was being generous. I said, yes please go get your manager, and that I can't wait to show him this video and how rude you are being. He said he would go get his manager, but the gate is closing in 5 minutes and that i was going to miss the flight. I realised he was right and tried to appeal to the lady who initially flagged me to him that I was allowed to check 3 bags. She said yes I was right, but he gave her an evil look and she quickly apologised to me and went away as everyone had boarded and her job was done. I had no choice but to pay at that point as I could not miss the flight.
However, when I got on the plane I complained to the the flight attendant. He saw what I had left as carry on and said that it was ridiculous. The flight wasn't even half full, and he moved me to my own row, sat next to me for 5 minutes after meals were served, and kept giving refilling my glass full of champers. He wrote the entire ordeal down in detail. He then watched the event on video and agreed that the guy was a total jerk. He advised me to write to Qantas, and then he wrote to Qantas on my behalf as well and CC'd me in on the communication. I also note that after traveling on 8 flights within South America, then my flights back to SYD back through AKL I took the carry on load out that I was denied on this flight with no problems.
This all happened on May 17th. On Friday I got a call from Qantas customer service. They firstly said that they were impressed by how detailed my email was. Especially that it was specific with names, dates, and flights. It seems this is key as many people are not and just give generally descriptions of people they dealt with. Secondly they apologised profusely because this guy was in the wrong. Thirdly they said that this guys manager and department(ground staff) had been notified and given all the information, and that he would be dealt with. Lastly they refunded me my $150. It took a while for Qantas to get back to me, but they did. Write to them. Be specific. I asked them if they wanted the video of the incident, but they said it wan't necessary. That was disappointing, because the guy just got more belligerent because I was recording. He kept saying it doesn't mater if I take his name and recorded all I want, I'm still paying the $150. I still get ticked thinking about it even though I schooled him in the end. I do wonder what, if anything, will be done in form of discipline. It was an appalling way to treat a customer and he seemed to revel in it. Like a piece of dirt I felt. coughpy way to start the holiday, but was great from there on.
The situation is a little different to yours, but my point is that he was in the wrong, and I bet Qantas rights the wrong if you write a thoughtful letter. Make it detailed. I hope you took names, or even video!