Finally got to the bottom of this problem... and come to find out its not a problem. Some background:
The Nismo R-Tune 1.5 Way LSD has three adjustments for preload - Low (51 ft. lbs.) Med (69 ft. lbs.) and High (101 ft. lbs.). Before the last even I had been running the diff set at Med which worked fine, except for a small push on corner entry, at the previous track events. For this Cal Speeday event I backed off the adjustment to Low to reduce the push and get the car to turn in a little better. At the track, the diff worked fine and the push was reduced.
My 350Z is at Unitrax and they pulled the diff, tore it down, and inspected it. There's nothing wrong with the diff and its odd street driving power on/off behavior is the result of the design and me having the diff set on the Low setting. The best Unitrax can figure is that the combination of vehicle weight, engine torque, and differential design (ramps and preload adjuster) has the diff locking and unlocking randomly under part throttle. A lot of that may be because the preload adjuster is a poor design and doesn't appear to work properly on the low setting. They think it might be allowing 0 or 51 ft. lbs. of preload.
Anyway, I'm going to pull that diff and sell it on eBay. Unitrax is installing an OS Giken Super Lock LSD in my 350Z: http://osgiken.net/products/superlock.html