The XUV is about 60 inches wide and I think the space between your wheel wells is 48 or more inches (they still make it wide enough for a sheet of plywood, don't they?) which leaves 12 inches, or 6 inches per side. Not quite enough for the tires to ride up over. I'd suggest creating some wood ramps or "speed bump" to support the inner half of each front tire as it tries to run up over the wheel wells. This will add support and it will make it easier to load. If you get off one way or the other with only half of each tire supported, it'll want to slide the machine off one wheel well and you don't want to bump the sides of your box nor do you want to mess up the Gator.
Also, pay attention to your owner's manual which shows a picture of a Gator loaded on a flatbed truck -- backwards. I believe John Deere recommends loading these machines backwards becahse the engine and transmission weight are rearward biased and you want that weight as far forward as possible.
And remember that a 1600 lb machine with rear weight bias has, say, 1000 lbs on the rear axle. Are you confident your tailgate can support that? Or will you remove that instead? And your ramps are sufficient? And you have tie down points with strong straps?
I'm partial to trailers for hauling equipment, but if you manage to do this and do it safely, post your story here so we can learn from your experiences.
Good luck.