UPDATE: It turns out to be the intake cam phasers were damaged. Shop replaced the intake cam phasers, timing chain and tensioner and we went ahead and replaced the oil gallery gaskets and bolts. Total was about $3800. The P0011 code is gone, drove it home and it felt great. Hope that fixes everything.
Note: Shop mentioned that they did the same repairs on about 7 other 370z's already. This shop is Z car specialty repair shop.
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