Dual Monitor Setup, One Monitor has Double Width and scrolls into other monitor
Solution 1:
I've figured out what was wrong after trying a few things. I had to plug both monitors into the same kind of port, on the same graphics card. I had a hard time digging up the cables at home but once I got my hands on a pair of HDMI cables, I was able to set up the monitors correctly without much trouble.
It seems obvious now in retrospect but this didn't occur to me, especially since my Windows install on the same machine seemed to handle the original setup (two types of ports, two different devices) well enough. This makes perfect sense though.