Spohn, only exposure to the situation that creates the anxiety will work, especially if it is repeated with short intervals in between the trials.
Since you have a safe closed course to try, I'd say schedule several runs a day for as many days as you can, starting slow and building up to pushing the limits.
Good luck and keep us posted
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Rain, snow, sleet, hail: 2009 Mazda 3 sGT HB
Everything else: 2009 370z, PW Touring 6MT