I don't think there is any way to ship a replacement under GSP. If you just sent a replacement to KY they wouldn't know what to do with it since it isn't tied to an eBay transaction. I doubt they would return it to you either.
I don't know what the battery is worth, is it even worth getting back if it's not in good working order?
In a Not As Described situation (except damage in transit) you would be on the hook for the return shipping cost and for International it's likely to be quite expensive.
Paranoia strikes deep
Into your life it will creep