I'm amazed that I hadn't found out about this already, but I found out today that NASA Texas offers a Time Trial program!
Time Trials are a cross between autocrossing and DE events - competitors are on the track at the same time, much like a DE-style format, with passing only allowed in certain areas (i.e., no banging fenders for position). However, all cars are fitted with transponders, and there is timed competition against the clock, with different classes based on car and modifications. Entrants will get a similar amount of track time as HPDE drivers (typically 3 or 4 20-minute sessions per day), but the only difference is the competition angle.
Their last event of the '05 season is November 5-6 at Motorsports Ranch. I'm going to try to make this, either driving my own car, or co-driving Billy's Honda Challenge Prelude. Anyone else interested in some high-speed, road course competition?