As soon as I posted that last screed, I tried a few more combinations of export options. I got a magic combination!
In Illustrator, Export as TIFF, set the colorspace to Grayscale, 600dpi resolution, anti-aliased, IBM-PC byte order.
Or not. Crap. I just tried to save, and it bleeped at me several times saying that it didn't support LZW compression. When I closed and tried to reopen the file, the brace was gone.
Have I done something really wrong to deserve this?
Oh cool. Now it just blanks out the graphics as soon as I place them. What a fantastic piece of software.