Ive driven trails there twice with similar size tires and had no issues. Just me, the dog, a cell phone, GPS, water, rope and shovel. Most of the trails I explored were mapped on the GPS.
Being alone, I avoided and drove around any spots I thought looked to soft, and or muddy.
I have heard the stories of people living out there, but I saw none and wasn't bothered at all! I did see several areas where idiots dumped trash and left trash after camping. Could never figure out why anyone would go way out to enjoy the solitude of the wilderness and leave trash behind?