As stated tracks with rules against clinchers is due to both safety and the damage caused by a blow out with a clincher where you will fall off and then maybe take down all the people behind you. Tubs you have a fighting chance of staying up. To be honest I am not sure that there are that many tracks that would continue with this rule however but old habits die hard.
I would second the veloflex with latex tubes route, or I have uses conti supersonics with latex as well. Most of the high end tyres will be fine but I have a soft spot for the veloflex.
Just as an aside, I was training by myself on one of our club bikes tonight doing flying 1 lappers. I thought the bike I was on had a creaky bb, but as I came around the home bend at full noise, my left arm crank came off. With the crank flapping in the breeze, all I could think of was what sort of big crash would you have if your right hand crank came off with a fixed wheel!!! Anyway if its not your bike check all the bolts - there are not that many on a track bike
