You should take a look at the
Goodyear GS-D3. They are just under $1000 as well.
If you take a look at the Customer Reviews all of the Corvette owners really seem to like them and rate them very highly. All said they were major improvements in the areas you mentioned over the OEM run flats.
You can read the reviews from Corvette owners by going to the
Goodyear Eagle F1 GS-D3 page, clicking on "Read all reviews for this tire", then filter by Make and select Chevrolet. Almost all of the Chevy reviews are from Vette owners.
-Scott