We are hoping for a trip to Lake City, CO for the July 4th holiday to ride our RZR 4 on the Alpine Loop. Everything apparently is booked a year in advance so we are wondering what our chances would be of finding a campsite (in a BLM ground or dispersed) if we arrive on Wednesday the 1st. Maybe we'd be a little ahead of the crowd? Anyone have any suggestions? We are from Monument, CO and don't want to drive 6 hours and have no place to sleep. Thanks!