As far as I know, insurance agencies do not cover track eventualities. You will need to get track insurance.
See this thread for more info about insurance on track days
http://www.ft86club.com/forums/showthread.php?t=9523
Lockton seems to have track insurance on a event/event basis.
I put in $30000 as agreed value and got $210 as a per-event cost.
http://hpdeins.locktonaffinity.com/Default.aspx?cID=3
Whew but hey, you pay to play right?
It's expensive but $200 is worth the peace of mind and pushing the car without worrying about balling it up and losing $27 - $28k in a single day!