I think if you do this sort of pleasure driving a lot then you probably should invest in an engine oil cooler. Since this is southern California, I don't think you need to worry about a thermostat for the oil cooler like you would on the east coast.
For the diff cooler, I would say you probably don't need it for street use or even casual track day use, but if you were doing track days with back to back sessions, or if you install a conventional clutch type LSD, yes then for sure as these run much hotter than the stock VLSD.
The reason is we noticed that early pre-production vehicles had both diff coolers and engine oil coolers. From some of our experience racing 350Z's and 300ZXes, we have noticed that the 350Z runs way higher diff temps than the older cars because the diff is tucked up high in the body structure and doesn't get much air flow exposure. The 370Z is exactly the same in this respect. The 350's raced in SCCA T2 class and Koni Challenge were plagued by diff failure, usually the diff locking up! Sometimes in as little as 30 minutes of continual track use. In these racing classes, particularly T2, the cars are in pretty close to stock condition.
When working with Steve Mitchell's time Attack 350Z, we had to continually monitor diff temp with thermal indicator paint, stickers and an IR gun and run carefully as not to exceed 20 minutes or so to avoid diff failure. Eventually Steve went with a diff cooler.
Since the 370Z uses the same short nose R200 diff and has a high out of airflow position as the 350Z, and after seeing the cooler on the prototypes, we can assume that the 370 is going to have the same diff temp issues as the 350 did under track conditions. I personally feel that for street use, even hard driving that you will be ok but like I said for track days, avoid doing back to back sessions.
You might want to investigate if the Nissan Motorsports Euro rear diff cover for the 350Z will fit. This gives 1 quart more sump capacity and has cooling fins. This is a stock part on euro Z cars. Its not enough for racing but it might be a good compromise for the street. Greddy also makes a big pan with lots of fins and an even bigger sump but I don't know if their is chassis clearance in the rear.
Also run high quality synthetic gear lube.