I'm a member of a club that has in the past had their own "trackday". To be more precise what they have done is approach an established organiser and basically booked out an entire session between them. This way you avoid all the problems with insurance and liability, plus it's down to each individual to pay their way. Worse case scenario there isn't quite enough of you to have complete exclusivity, but it's surprising how easy it is to gang up on an interloper should their behaviour not fit in with the group etiquette.....