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I don't trust dealers to do alignments, especially under warranty. Looking at your specs, I wouldn't settle for "No Alignment Necessary."
It's not symmetrical, for one thing. Look at your rear camber, its positive one side and negative on the other.
However, if it is really behaving as you describe, it sounds like something is loose. I would especially look for rear toe and camber adjustments. It could be the bolts that hold the hubs to the knuckle.
Upper control arms can produce very unsettled behavior if they are loose. All of these things have happened to me, although not on a C7, but since there is so much similarity I would have to assume these things are still possible. They would not necessarily show up on an alignment machine because it is taking static readings.
I wouldn't obsess over the castor: that can't be adjusted independently, anyway. The tires could be the problem with a damaged belt, but I would think an examination would find that.
I would be looking for something that causes the toe or camber to be changing while driving. I would also put a little toe-in in the rear, even if you do find the problem and fix it.
Not a very good printout as it doesn't show the numbers. Being in the green doesn't mean much since the tolerances are very wide. Funny that they didn't measure front caster while they had the machine hooked up as all it takes is to mover the front wheels back and forth in a +/- 20 degree arc. Close to a minute total with *** scratching time taken into account.
Tire pressures are at 30 lbs. C7 is Z51. Am running stock tires. The sensation happens on all road surfaces but is pronounced at highway speeds. I have taken it to the dealer and had the alignment checked. The only alignment spec not checked was caster. I am also of the opinion it could be a bad shock or bad anti-sway bar. But it is hard to believe this would be the case at 1600 miles. I am stumped. The car just feels loose and certainly not like a sports car should feel, expecially a Corvette.
Switch it to sport or track setting and see if that help.