Digging around I found a thread where customers were wondering what happened to bridge mode and why it had been removed. An obdurate admin informs everyone that D-Link decided it wasn't needed as a feature, so they removed it. The admin is very coarse and ends up locking the thread.
It seems ridiculous that, for a hardware product, a company would decide to remove features in a firmware upgrade. There is a work around, but even if it is a legitimate thing to do, it seems like a terrible product and engineering culture to be this condescending to customers.
Relevant thread: http://forums.dlink.com/index.php?topic=4542.0
End of story: The router ended up going in the trash after other issues, along with two different D-Link models.
It's not the best idea to use consumer grade gear in an office, but then I replaced it (as a temporary fix) with an even older Linksys WRT54GL flashed with DDWRT with no problems.