REST API: Creating a Sales Order with a Contact_Name

REST API: Creating a Sales Order with a Contact_Name

Hi, I'm trying to use the REST API via Postman to load some historical sales orders.  I have a basic example working, but when I try to specify a JSON object for the Contact_Name field (so I can link the sales record being created to a contact), I get the following error:
{
    "data": [
        {
            "code": "INVALID_DATA",
            "details": {
                "api_name": "Contact_Name"
            },
            "message": "invalid data",
            "status": "error"
        }
    ]
}

Here's my JSON (I believe Web_SO_Number is a custom field we added):
{
  "data": [
    {
      "Owner": {
        "id": "5027237000000365009"
      },
      "Contact_Name": {
        "id": "2165315000025476001"
      },
      "Purchase_Date": "2021-09-21",
      "Subject": "Original Order 3",
      "Web_SO_Number": "G-9209",
      "Status": "Shipped",
      "Product_Details": [
        {
          "product": {
            "id": "5027237000000399428"
          },
          "quantity": 1
        },
        {
          "product": {
            "id": "5027237000000399429"
          },
          "quantity": 1
        }
      ]
    }
  ]
}

I'm following the example in the official Postman workspace which shows this:
{
  "data": [
    {
      "Owner": {
        "id": "{{user-id}}"
      },
      "Deal_Name": {
        "id": "{{deal-id}}"
      },
      "Account_Name": {
        "id": "{{account-id}}"
      },
      "Quote_Name": {
        "id": "{{quote-id}}"
      },
      "Contact_Name": {
        "id": "{{contact-id}}"
      },
      "Discount": 127.67,
      "Description": "Design your own layouts that align your business processes precisely. Assign them to profiles appropriately.",
      "Customer_No": "Customer_No",
      "Shipping_State": "Shipping_State",
      "Tax": 127.67,
      "Billing_Country": "Billing_Country",
      "Carrier": "USPS",
      "Status": "Delivered",
      "Sales_Commission": 127.67,
      "Due_Date": "2018-01-25",
      "Billing_Street": "Billing_Street",
      "Adjustment": 127.67,
      "Terms_and_Conditions": "Design your own layouts that align your business processes precisely. Assign them to profiles appropriately.",
      "Billing_Code": "Billing_Code",
      "Product_Details": [
        {
          "product": {
            "id": "1000000071967"
          },
          "quantity": 150,
          "Discount": 20,
          "product_description": "product_description",
          "Unit Price": 10,
          "line_tax": [
            {
              "percentage": 10.5,
              "name": "Sales Tax"
            },
            {
              "percentage": 6.5,
              "name": "Common Tax"
            }
          ]
        },
        {
          "product": {
            "id": "100000008007"
          },
          "quantity": 151,
          "Discount": 21,
          "product_description": "product_description",
          "Unit Price": 11,
          "line_tax": [
            {
              "percentage": 11.5,
              "name": "Sales Tax"
            },
            {
              "percentage": 7.5,
              "name": "Common Tax"
            }
          ]
        }
      ],
      "Subject": "Subject",
      "Excise_Duty": 127.67,
      "Shipping_City": "Shipping_City",
      "Shipping_Country": "Shipping_Country",
      "Shipping_Code": "Shipping_Code",
      "Billing_City": "Billing_City",
      "Purchase_Order": "Purchase_Order",
      "Billing_State": "Billing_State",
      "$line_tax": [
        {
          "percentage": 12.5,
          "name": "Sales Tax"
        },
        {
          "percentage": 8.5,
          "name": "Common Tax"
        }
      ],
      "Pending": "Pending",
      "Shipping_Street": "Shipping_Street"
    }
  ]
}

So as far as I can tell, I'm filling in the Contact_Name field correctly, but I still get an error.  If I remove that field, it works.  I have confirmed the contact ID I am specifying exists in the sandbox I'm working in.

Thanks for any suggestions.