They make you mad, don't they. They must believe you are going to clone yourself for the flight.

Problem is you can't prove whose mistake it was, and that may as well mean it's yours (without getting into technicalities I certainly wouldn't understand). With that in mind there will be a ridiculously small amount of cost incurred by the airline, and they are quite entitled to charge you for it. I bet you would happily pay thier true costs, eh!
Not many people understand the re-selling thing and go mad, kudos to you for not doing so (I'd have gone grrrrrr etc)

As you may have picked out, this perfectly good reason is used as an excuse by the airline to cover every eventuality, thus stopping people re-selling and all the while racking up profits.

Well, racking up dosh they don't really deserve, at least.
I would think the whole business is knocked about as a service, and wouldn't rate your chances of getting it back.

I would point out that they are advertising the fare cheaper than they are stating, and are willing to pay that partial fare increase.
One good thing is, should you now choose to not take the flight, all your APD will be returned no questions asked. Most airlines will not, Easyjet will. (All Airlines refund it, but most of the tea-leaves impose an Admin fee that is always the same, or more, than the refund amount).