Thanks for following up, CompoundCarl.
The weird thing is that sometimes things are perfectly centered. I actually printed a PLA temperature calibration tower last night on the right extruder to test my new cooling duct and it was perfectly centered.
While writing this, I actually loaded up the large print on the left extruder (loaded the file in from scratch), and it printed off to the side again. Figured I might as well test the right extruder with the same file and it was off the the side too, but at least fully on the build platform (by 1mm). If you'd like to run your own test (just to print the outline), I'm trying to print the "stand.stl" file from here:
http://www.thingiverse.com/thing:1153855/#files (rotated X: -90, Y:90 and uniformly scaled to 90%)
Unfortunately, this is not the first file to print off the the left. I had noticed it with multiple other files, but they were all small enough that it didn't matter. I figured maybe it was some quirk in the software since I was always using the left extruder, and it would be fine when printing something larger.
While we're troubleshooting things, S3D almost always continues to show that I'm printing after the print has completed or been cancelled. It can stay that way for hours (sometimes I'll start a print before bed and it still reads as printing in S3D when I wake up). I have to go into the Machine Control Panel and disconnect/reconnect. It's not every time, but I'd say about 80%.
Speaking of the Machine Control Panel, is there any way to remove the Bluetooth port or at least set USB up as the default? I never remember to change it when I connect the first time (Which I'm surprised it doesn't connect automatically. Maybe because it's defaulted to Bluetooth?) and then I have to wait for it to fail the communication attempt before I can swap it over and retry.
Thanks again for all your assistance.