Now what? Knowing GIB doesn't play exclusion and probably has no good tools to continue, I just went ahead and bashed out Blackwood without checking things too closely.
Rather surprisingly, 4NT wasn't Blackwood. Can you guess what it shows?
Some nested spoiler tags for a slow reveal:
Spoiler
It's a close race between this description and the one where it promises 14 cards, but this wins for me.