I've done "track days" twice, both times on rented bikes, R6s. First time: maybe the most fun I've ever had on a bike. Second time: damned glad I was on a rental, the damage to it was minimal (these are prepped for crashes), the damage to me more significant - sprained right-side ribs, front and back. Ouch! But I did see FJRs out there and they held their own.
If you run the FJR, I suggest removing all plastics and other items such as mirrors and windshield that could suffer in a get-off. Maybe even the headlight module, tail lights, etc. I would surely not run without frame sliders, and swing arm and fork sliders might be a good idea, too. If you have an older retired helmet, you might want to use that instead of risking your new $800 Shuberth or whatever. Make sure your gloves have full gauntlets that tighten very securely around your wrists. Take some food, snacks and plenty of hydrating fluids - water, gatorade...
Your 2014 is a pretty valuable device to risk this way. I know of no standard insurance that will cover damage on a race track. If only you had a 2003 with 238,000 miles... then, no biggy.
Some places allow good textile riding gear instead of full leathers, especially if the jacket will zip to the pants.
Others with more experience and better thinking will likely be along shortly.
Do it! Good luck! Have fun! Report back!