Someone at Ikea really dropped the ball on this one. Maybe try calling again and speaking to a manager? It's not clear in the letter whom you spoke to and I'm wondering why any manager worth their salary wouldn't jump on the offer of a customer paying shipping (Which, by the way, was overly generous and thoughtful on your part IMHO).
I've had small problems with Ikea of Conchohocket and Ikea of Newark when I lived in Jersey, and they've always sent missing pieces, one time they tracked down discontinued bookcase shelves for me from several stores which saved me from having to get a whole new wall unit set. I've always been pleased with their quality and customer service, So I'm shocked to hear their refusal to help.