Just an update... I got an email from them on 10/4 saying that my dispute was resolved in my favor and that the $100 was applied to my account. Just one problem... I never received the money! So I called again today. Went through about 4 CS agents, one of whom tried to say that the promotion didn't apply to me, before I finally got a manager.
It turns out that the money really was applied to my account, but the only way to access it / see it is by logging in to card.apple.com, going to Settings, and it is listed there. Then you can apply it to your statement balance. Really terrible implementation, but at least it finally worked.
Still, this really reflects poorly on Apple... I know it the card is a Goldman Sachs product but it has Apple's name on it and they should do something about the terrible customer service that GS has. I can't believe how much time I wasted chasing down this stupid bonus. Now I'm reconsidering using this card to finance future Apple purchases.
Also this is petty but their "on hold" music is terrible and starts over every time they put you on hold. Almost designed to infuriate.