D'OH! Thanks, silverfox!
I did have "Search online automatically when connected to the Internet" checked. And after unchecking it I can work locally with normal response time.
I will say that further clarifies the bug in FTM 2014. If I say "Go Offline", then it *should*... GO OFFLINE. But the "automatic search" logic ignores my choice, instead it is just checking if the Internet itself is reachable.
I had thought about just unplugging the network cable, and based on this result I'm pretty sure that would work too.