Insuring Trade-In Question

I recently purchased a new iPhone from the online Apple Store, trading in my iPhone 13 under the AT&T $1000 trade-in offer. I am getting ready to send my trade-in phone in via the UPS trade-in kit. I would like to insure the trade-in for the $1000 value, but have been told I cannot purchase additional insurance when using the prepaid UPS return label. So, I am considering boxing the provided prepaid box with label inside another larger box, and paying for the shipping myself with insurance. Has anyone successfully traded in a phone this way? It is going to the Jefferson, IN trade-in site.