Hey BRN, welcome to the forum.
I hate to "scoff" at this, being your very first post and all, but you asked.
Why? Why throw a hitch on your G when you already know that Infiniti doesn't recommend it?
Okay, I'm done now.
I'd start by contacting Infiniti to find out exactly what the tow capacity would be. You stand a chance of overheating the transmission which can cause damage and being that you have an X, you stand a real chance of damaging the AWD system as well.
I think the short answer here is, don't do it! At the same time, we're only talking about 1,100 lbs. Would Infiniti not sell a G to a family of people weighing 300lbs each?
For more info than that, I'd ping Infiniti.