You may be a bit short on capability with your GC. I tow our FC23FB with a 2014 EcoDiesel GC and find it more than capable. Great, actually. However, the diesel has 7200 lb tow rating and 720 lb tongue rating. Search my posts for performance details. The actual tongue weight of the FC23FB is higher than the brochure states. My tongue weight in camping mode is 785 lbs. Add your particular hitch weight to that. Mine with an equalizer hitch comes to 876 lbs. which is over my 720 lbs stated tongue capacity, but has proven to be no problem in over 20,000 miles of travel.
Joe & Joan Donnaway