Thanks for the reply. Here's what I ended up getting:
HDMI port -> HDMI cable -> HDMI female to DVI-D female adapter -> DVI cable -> LCD
Thus, I ended up with inexpensive, silent, dual DVI, plus an on-board VGA port which is useful in my application. (Note that this does not allow simultaneous triple-monitor use, but does allow one to use any two simultaneously just by using the ATI Catalyst software)
Though right now the fanless card is the hottest thing in my box and it looks like I might need to add another quiet fan somewhere to keep the case/mobo temps down.