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Obviously, there is more to tire sizing than just width. You need to use a lower profile tire than the stock tire. If you have 19" wheels on the rear of your Stingray, you can run 305/30R19 tires without rubbing. I have done this on my car with no rubbing under all driving conditions. 305/35R19 tires will be too large in diameter and they will certainly rub.
If you have 20" rear wheels which are stock on the later Stingrays, you would need 305/25R20 tires which I do not have any experience to share with you. Mounting 305/30R19 tires on the stock 10" wide rear wheels is challenging because the tires are pinched on those wheels. But is is certainly possible and it looks and works well. Mounting 305/25R20 tires on 10" wide wheels sounds like a serious pain due to the short sidewall height, but again it should be possible. You would need someone who is really good at tire mounting to do this and not damage the tire or wheel.
Technically the rim width range specified for 305 width tires is 10.5 to 11.5 inches. That means some shops may refuse to install those tires on your wheels since the manufacturer of the tires says this is not recommended.