+1 on getting an Oil Analysis if you are debating when to change your oil this much. It will tell you how much life is left in your oil if you changed it to early or how much life is not left if you waited too late. Then you will know based on your circumstances when the optimal time is to change your oil. Rule of thumb is to change it more often than not.
Now I want to know why none of you are changing your oil after driving around the block for optimal performance!
2011 Nismo#91, What did your analysis show as far as percentage of contaminants in the oil after 3000 miles? I am guessing that driving such few miles it would be low. However for the guys storing their Z's for the winter after driving it all summer. I would recommend changing the oil prior to storage if you aren't already doing so. This will prevent potential contaminants from settling and causing harm to the engine.