I'm currently trying to organize a private track day at NOLA Motorsports Park for some time in 2016, currently (Dec '15) thinking probably around early Fall.
The price will depend entirely upon the number of people participating, but you can expect it to cost more than a normal track day. But, instead of a handful of 20 minute sessions, you'll get 8 hours of seat time for the day. I have an approximation of the total cost for the day, which I don't think is necessary to share right now, but if you would seriously be interested in paying a good chunk of change for an open track with several other 86 drivers, please let me know. My realistic goal is to get the cost down to $500 per person, but my ambitious goal is to get it down to like $300 per person. As I said though, final cost is completely dependent upon participants.
Included in the total cost of the facility is the covered paddock area, which is typically reserved for high end cars/professional race car drivers, from my experience. So it'll be awesome to be able to park under there.
Also, we could probably have the event catered if that's something people would be interested in. I think it could make for a really fun and relaxed day for everybody; a good bonding experience, plus a ton of track experience.