Have you reviewed the fare rules and contract of carriage? That is what would apply, especially if you wanted to make a DOT complaint. I think that unless the website specifically says that you can do what you are saying then COPA only has to what's in the fare rules.

I had a related situation a year or so ago when I had a ticket that was mixed UA and CM. I just wanted to make a change that affected the CM flights and was told that I would have to pay the higher UA fee of $200. When I went back and read the fare rules, it was clear that they were correct that the ticket would have to be reissued by UA as well as COPA. I thought I had a case because the website said the fare change was $115, but I got nowhere,

Given what I have read about dealing with COPA by other posters, unless the fare rules are explicitly in your favor, I would not hold out much hope.