Personally, I'd rather make some money off of one of the sets of wheels. They will be worth more selling as a staggered set than selling all four fronts. But if you are going to keep both sets and don't mind storing the 4 front wheels and run the square setup you mentioned, you will get some poke at stock height, I'd expect, on the front. The smallest I'd go on the 10" wide wheel is 255/35, if you want no stretch. I've done this setup before and it works. That should fit ok up front.
Have you tried taking one of your 19x10's with 275's on it and put it on the front? Then you'd know how it will fit.
If it were me, I'd keep it staggered and sell a set of your Rays and use that money for a good set of tires or coilovers/springs.
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"Let me tell you something. Anyone who owns a car like this (370Z) has something wrong with them in the head." My Grandpa who has owned 4 Z's in his day. 
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