Specify [shipping] in JSON-LD Product for Google

Question

I am implementing JSON-LD product data on an e-commerce website and having trouble specifying product level shipping cost. Google's Merchant Center document states that a [shipping] attribute may be used "when the shipping settings aren’t defined at account level in Merchant Center or if you wish to override the account level shipping settings for individual products" (emphasis mine). I've implemented this attribute, but Merchant Center is still showing the (higher) account level shipping cost for all products.

Here is an example:

<script type="application/ld+json">
  {
    "@context": "https://schema.org/",
    "@type": ["Product", "Book"],
    "name": "Book Title",
    "image": ["https://mywebsite.com/img/products/1111BookTitle.jpg"],
    "description": "Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.",
    "sku": "9780000000000",
    "shipping": "US::Media:3 USD",
    "offers": {
      "@type": "Offer",
      "url": "https://mywebsite.com/products/1111-book-title.html",
      "priceCurrency": "USD",
      "price": 25.95,
      "itemCondition": "https://schema.org/NewCondition",
      "availability": "https://schema.org/InStock",
      "shippingDetails": {
        "@type": "OfferShippingDetails",
        "shippingDestination": {
          "@type": "DefinedRegion",
          "addressCountry": "US"
        },
        "shippingLabel": "media",
        "shippingRate": {
          "@type": "MonetaryAmount",
          "value": 3,
          "currency": "USD"
        },
        "deliveryTime": {
          "@type": "ShippingDeliveryTime",
          "cutoffTime": "11:00:00-04:00",
          "handlingTime": {
            "@type": "QuantitativeValue",
            "minValue": 0,
            "maxValue": 1,
            "unitCode": "DAY"
          },
          "transitTime": {
            "@type": "QuantitativeValue",
            "minValue": 2,
            "maxValue": 8,
            "unitCode": "DAY"
          }
        }
      }
    }
  }
</script>

My expectation is that the above [shipping] should result in a price of $3 for "Media" service anywhere in the US, but instead Google shows $6.75 and I don't see any of my shipping data in the Merchant Center product listing. (I'm unclear if Google looks at [shippingDetails], but I included it for thoroughness.)

Any advice appreciated!