It's sad but, Goodyear, which once was a top notch OE ultra performance radial tire brand for Corvettes, has apparently, left both the OE and the replacement market for ultra performance tires. The F1 Supercar EMT, the OE tire on GSes, was a substandard product as far as tread life and noise.
Unfortunately, Goodyear has developed no new ultra-performance products since the late-00s and the last one GY did release was only used on the last of the base Z06es, that is: 2011-2013 without Z07. The GY F1 Supercar G2 EMT was a pretty darn good tire, but was Goodyear's last gasp before it ceded the Corvette OE and replacement tire market to Michelin. Nevertheless, as good as the GY F1 SC G2 was, it still cannot provide outstanding tread life with the Z06's aggressive front suspension alignment specs. In fact, no tire can do that unless the tread compound is rock hard, and...you're not going to see a "rock hard" tread compound on any Corvette tire unless it comes from some cheap-assed tire maker in Asia.
With respect to Grand Sports eating up tires, the problem is that, while the GS package replaced Z51, it also carried over the Z51's aggressive (i.e.: for the track) alignment specs. As suggested elsewhere in this thread, if your GS never sees the track and never gets run hard on the street, you'll benefit by degrading the alignment specs back to the front/rear alignments for the base C6. Yes, you will loose some of the car's cutting-edge handing at the limit, but you will gain tread life. For people who are willing to spend $60,000 on the car but don't want to spend 1500 bucks every 15,000-18,000 for tires and are willing to give up some performance handling, that is definitely the way to go.
Combine the alignment change with a switch to Michelin Pilot Super Sport tires and you'll be a lot happier, but keep in mind the better tread life is going to come mostly from the less-aggressive front suspension alignment and less from the switch from Goodyear to Michelin.
Keep in mind that, if you change your mind and decide to go to a performance driving school or take the car to a track day, you need to reset the front end alignment back to the recommended Grand Sport specifications before you go, otherwise your burn the front tires off the car in a very short time.