It seems common sense to pick up the phone when there is what is a "technical" error and before paying an extra $1,000.

At a minimum and before wasting time here on FT, I would be on the phone to AF and calmly explain the situation. You are correct that at this point, having paid, you may be SOL and have the choice of cancelling (24 hours for a US reservation which I presume from the $ costs) or not, but I cannot imagine not asking.