The most foolproof way to anneal case necks that I know of is to use a product called "Tempilaq". Basically, you paint it on, heat the area with a propane torch and when the lacquer melts dump the case into water.
Comes in several temperature ranges from 400 F to 1550 F. Takes the guess work out of the process by removing the subjective parts; when the lacquer melts you know that you've reached just the right temp - every time.
Available from Brownell's, Midway and no doubt others as well. About $10.75 for a 2 oz. bottle with a brush built into the cap. Will do a lot of cases per bottle.
IIRC, quenching is necessary for proper annealing. Air cooling can result in actually hardening the brass instead of making it more malleable.
BTW, have you done any surfing on the sites like Gun Broker, ammoman, etc.? Surely Cole's can't be the only option for FNM ammo. FWIW, I got mine off an ad at Gun Broker and ended up paying a lot less than $10/box even with shipping.