@SuperFromND Thanks!!! Your guidance led me to a solution.
Xinit was indeed the solution to my problems, and it actually ended up being very simple. I'll try to spell out everything that was done so anyone finding this thread can follow along the best they can.
OutFox/Stepmania works either from the startx or the xinit environments, but the following code is what allowed me to start the game from the emulationstation menu automatically. This is the contents of ~/RetroPie/roms/ports/OutFox.sh
#!/bin/bash
xinit /opt/OutFox/OutFox -- vt1 -keeptty -nocursor
The second argument is the location of the executable for outfox (if you have stepmania it will be the path to the stepmania execuatable). The last arguments keep a no-permission error from occuring.
Once this file is in that location, there should be an OutFox option to choose on the ports screen, and it should load OutFox properly. Surprisingly I didn't have to change any configs anywhere else, it just seemed to work like this for me.
Here's a post that I mostly used to get OutFox setup (there are plenty of other good tutorials for this too): https://www.reddit.com/r/Stepmania/comments/psd1hm/raspberry_pi_4_stepmania_outfox_53_guide/
I'm obviously a novice when it comes to this so I'm sure there's better ways of doing this, but this works for me so I'm happy.