I have been through box canyon many times but not in the liberty. You should be able to make it. We managed to get a patriot FDII through Box with no damage.
I did bulldog once but not in the liberty. I remember it was a pretty easy trail.
. They have lots of local runs including box canyon on a regular basis. I would run it with you when the weather cools a little. My 'off road' rig has winch/lockers/tow points and lots of recovery gear.
Here is a thread with the 'patriot run'. Don't be put off by the other rigs and the more difficult spots. Those are bypassed. Lots of patriot shots on page 2.
I have never seen a liberty run it but I really don't think it would be a problem and should be a lot of fun!