If he wants to just condition them, the track tac tire tuff would be better, but if he wants to add bite to the tires and toughen them up, the mint would be the better choice. If it were me, i would use the mint though as you suggested because it does make tires tougher and more resistant to cuts and things you would get on an abrasive or rough track but also gives them some bite. It really depends on what you would be using those tires for next season, i wouldnt use the mint on tires i plan on using on a high bite track.
Do you guys wrap your Burris tires in plastic or foil for the winter or let them sit open? Im worried that any prep that might still be in the tire could break down the plastic and pull it into the tire and ruin it. No scientific knowledge to back it up, just have had the plastic wrap stick to asphalt and sprint tires (Firestone and Bridgestone) after they sit for a couple months. Seems to almost get in the pores of tire.
We've got a conditioner that's heavy laden with oils for storing your tires. (Pink Panther Thick) TT Tire Tuff original works well also.
Keeping your tires from the elements (that includes air) is always a good idea. Wrapping them with Saran wrap helps, sure. If the prep is dry to the touch on the tire's surface, I can't see any harm in wrapping the tires directly -- I certainly would not do this with some preps while the prep is still wet. Putting them in a heavy black (uv protectant) trash bag, removing as much as as you can from the bag before sealing is a big help as well. Keep in mind, that you will probably be refinishing the tire come springtime anyhow. Sometimes we actually want our tires to harden up!