370Z engines tend to be noisy - if it's not the valve train, it's the clutch; if not the clutch, it's a rear wheel bearing, etc, etc, etc. It's a two-seat sports car, not a luxury sedan.
I'd switch to ester oil and see if that helps. If the noise went away, I'd stick with the ester oil. If the noise stayed the same, I'd go back to a cheaper high-quality oil and live with the noise. If the noise got worse, I'd shut down until I could get problem diagnosed. YMMV