If my monitor is already locked to 60 fps would my runs be unrestricted fps or 60 fps (if I set it to unlocked)?

Your monitor refresh rate is not the same as your in-game FPS

You need to set the in-game FPS limit to 60 if you want to submit 60 or TCO run

And remember that you need to have FPS counter visible on your video

Late but steam has an option to show your fps in Settings > In Game > In-Game FPS Counter [Top-Left]

well, that wasn't the issue (I already have that enabled), it's that my monitor can only go to 60 fps, although I decided to just go for 60 fps only

Oh i understand, as long as the fps is capped to 60 in the settings you should be okay, the fps counter is mandatory hence why i said how to enable it