If it is doing it with xexmenu, I think we can rule out F3 being the culprit. that being said, Aurora is a much better solution then F3, and you should consider switching. it has all sorts of nice features, and the file manager and loading times alone make it 10 times more awesome then f3. and with nova being developed, which I am talking with maester rowen now about maybe adding a feature to it where it will stop original xbox games from unloading the hud, and allowing you to change emulation profiles on the fly, which would also remove the getting on the computer to join the original xbox link room(Who knows if it will actually happen, But would be awesome if it did.), and the ability to chat with friends on link(Needs a chatpad, or usb keyboard, as onscreen keyboard causes issues with the plugin). The latest version of aurora has adjustable quick views which allow you to set up your own folder views like F3, it is the better alternative. The only feature it doesnt have is an option to rip games from the disk, but it isnt really needed, as all you have to do is copy and paste all the files from the disc into a folder in your game scan path, then rescan, it really cant be beat.
Anyway back to the problem at hand, when you say the xbox reboots, do you mean it like hard reboots, and starts glitching again, or it goes back to the dash. If it is the first option, I would be checking the launch.ini for FatalReboot=true option. This wont fix the game, but it would fix the reboot problem, as when that option is set if a game/app fatal crashes, it forces the system to reboot.