So I've discovered that a simple terminal command fixes the black bars on the left and right when outputting through HDMI. It's caused by the tablet outputting a 1280x800 display to a 1280x720 signal. This is easily fixed by changing the device's resolution with the following command:
wm size 720x1280
To revert to the tablet's original resolution, use:
wm size reset
You may need to run the "su" command first for these commands to work, and you do need to be rooted in order for it to work. This will cause some things to get wonky, like the nav buttons disappearing in landscape orientation or the status bar being hard to pull down (perhaps solvable with a change to the DPI), but if you're planning to use this trick for gaming (which was my reason), using something like Smart Launcher 2 with a controller makes this a non-issue. If you want a quick and easy way to switch back and forth, try QuickTerminal on the Play Store and set up both terminal commands as "Quick Commands", or at least that's how I've done it. Now, the picture on your TV will fill the screen. This is as close to Console Mode as we'll probably ever see on this device, so I thought this might help a few people out!