Nitrogen lets the tires have a higher cold pressure without over inflating when hot, less pressure growth. The problem with sticky tires is that when parking with hot tires, they will stick to the floor and pull some rubber off when next moved. It is a problem in hot climates such as Palm Springs in the summer even if not driving hard just prior to putting away.
A possible solution is to put down something slick and smooth, such as plastic bags, to put the tires on. I have not tried it but it may keep the tires from sticking and chunking anything off of them, worth a try once.
I do not think the "out of round" concern is any problem. With race tires, we either put the car up on jack stands after the initial heat cycle, remove them from the car for 24 hours to cool down or roll the car back and forth every 30 minutes for awhile during the cool down if the tires are going to stay on the car and be used that day. Letting them cool down for one or more days after the initial heat cycle is prefered. The other idea is to purchase them already heat cycled. Tire Rack offers that with race tires. Heat cycling does require getting the tires up to temps and that can be tough to do on the street but it can be done.:biggrin
Using a pressure gauge to be sure they are up to temps is important if you don't have a temp guage, however.
Let us know what works.
"Big Dog"