@Russ I currently do not have the parameters enabled, but before creating this post, I did try out exactly what you'd suggested (I enabled parameters and set the off-command to be identical to the command), but the behavior was the same, the "view runs" logged the command being sent from HA, but the "Runs" count didn't increment.
Feel free to let me know if we should just give up on troubleshooting this. I'm sure you have more important things to do and I now know that I can disable the offline component as a functional workaround.
Otherwise, I'm happy to keep digging and will perform any troubleshooting steps/provide any logs or screenshots you request