Different situation altogether. Gifting someone something, they haven't sent you an amount to consummate the exchange, doesn't create an exchange of value. You could claim an item is 100x actual value and try to collect. Problem is the insurer will push back, question the stated value, and want to see appraisals of same type of item.
You paid $X for the grille + shipping and handling/packaging. Your total loss is exactly what you paid. You generally don't get the benefit of an inflated value just because you say so. There is a legal concept called unjust enrichment. You mention that the grille was impaired... so what is the actual value of said grille purchased? UCC is the legal controlling statutes here. I'd almost bet there is language in the fedex bill of lading/shipping agreement that addresses "value" as well.
I understand your position, it's a losing one IMO because the insurance isn't stated value. Otherwise the industry would be out of business from people sending $5 trinkets, claim they are worth $1000 and inflated claims being paid. Notice they want proof of payment/invoicing for a reason.