I'm Stupid. Nevermind. It turns out that the NVS 300 and some FirePro cards have separate DisplayPort channels now rather than passively converting DVI.
You can indeed use a DMS-59 to Dual Display Port adapter to get two fully functioning DisplayPort channels. You *do* need to use a good adapter though. There are lots of those out there that have odd issues above 1600x1200 resolutions (there's a few forum posts about this out there). A lot that I see recommended is HP part number XP688AA. It's pretty expensive ($30) but is guaranteed to be used with 2560x1600 resolution monitors.
Last EDIT to answer your last concern. It appears that in all likelihood the DisplayPort system in the card won't allow mixing of signaling (since they are designed to be output from a single port). You could try a passive adapter, but I'm guessing it wouldn't work.
With access to two fully functioning DisplayPorts, you can always connect your second monitor with an Active DisplayPort adapter.
Active DisplayPort to Single Link DVI Adapter:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814999030
Active DisplayPort to VGA Adapter:
http://www.newegg.com/Product/Product.aspx?Item=N82E16815158150