Thanks chewitt. As this happens to be a 4:3 CRT TV that has the ability to display 720p content, it gets letterboxed, and by playing 4:3 content inside of it, it will get columnboxed.
That being said, I ended up writing some scripts that allow me to easily switch resolutions by automatically SSHing into LibreELEC, mount the config, edit the relevant lines, and reboot LibreELEC to ensure the proper resolution. A small wait, but I can be patient 
I have a Raspberry Pi running LibreELEC Omega, and it's outputting video to my CRT via a VGA HAT. In order to set a resolution, I define the following in config.txt:
640x480 (4:3 content):
dtparam=hactive=640,hfp=20,hsync=66,hbp=74,hsync-invert
dtparam=vactive=480,vfp=7,vsync=1,vbp=37,vsync-invert
dtparam=clock-frequency=25194000,rgb8881280x720 (16:9 content):
dtparam=hactive=1280,hfp=76,hsync=60,hbp=248,hsync-invert
dtparam=vactive=720,vfp=1,vsync=3,vbp=22,vsync-invert
dtparam=clock-frequency=74490000,rgb888However, setting a resolution via config.txt only allows me to set one resolution at a time.
How can I set two resolutions? Normally I would set a modeline using xrandr, but xrandr is not found on Omega.
Much obliged!