NetSuite SuiteTalk Joined Search on Custom Objects

Question

I have two custom objects. The parent object is an Order, and it has a list of type Part associated with it. I'm trying to get the list of Parts with a value "Inventory Item" in one field, but only for a particular Order.

I have the name and numeric internalId of the Order available,but the problem is those aren't (as far as I can tell) searchable "fields", there is no "internalId" to provide to tell it to search on one of those.

In the code below, if I don't include the attempt to search on the Order it works fine. I can get all the Parts with a type of "Inventory Item".

I think I need to use a joined search? My attempt at it is below. This produces a SOAP error at runtime:

Additional information: org.xml.sax.SAXException: 'customizationRef' on
 {urn:common_2015_1.platform.webservices.netsuite.com}CustomSearchJoin is
 required

Code

private static SearchResult NetSuiteSearchOrderItems(NetSuiteService netSuiteService, string order_name, string order_internalId)
{
    CustomRecordSearch searchParts = new CustomRecordSearch();
    CustomRecordSearchBasic basicRecordSearchParts = new CustomRecordSearchBasic();
    basicRecordSearchParts.recType = new RecordRef { internalId = "64" }; //"Order Item" NetSuite Type ID

    //adding a search filter on a String Custom Field
    SearchStringCustomField partTypeFieldSearch = new SearchStringCustomField();
    partTypeFieldSearch.@operator = SearchStringFieldOperator.@is;
    partTypeFieldSearch.internalId = "896"; //ID of the Part object's "Type" field
    partTypeFieldSearch.operatorSpecified = true;
    partTypeFieldSearch.searchValue = "Inventory Item"; //only want inventory item parts


    //Show me only parts on a certain Order                           
    CustomSearchJoin orderSearchJoin = new CustomSearchJoin();
    CustomRecordSearchBasic orderBasicSearch = new CustomRecordSearchBasic();
    orderBasicSearch.recType = new RecordRef { internalId = "56" }; //"Order" NetSuite Type ID


    //--   WHAT GOES HERE INSTEAD OF SearchStringCustomField?

    //adding a search filter on a String Custom Field
    SearchStringCustomField fsoItemTypeSearch = new SearchStringCustomField();
    fsoItemTypeSearch.@operator = SearchStringFieldOperator.@is;
    fsoItemTypeSearch.internalId = "name"; //I have the "name" and numeric "internal id" of the order available.
    fsoItemTypeSearch.operatorSpecified = true;
    fsoItemTypeSearch.searchValue = order_name;//search filter value

    orderSearchJoin.searchRecordBasic = orderBasicSearch;

    //add in the things we want to search on
    basicRecordSearchParts.customFieldList = new SearchCustomField[] { partTypeFieldSearch };

    //add the basic search and join search and then perform the search
    searchParts.basic = basicRecordSearchParts;
    searchParts.customSearchJoin = new CustomSearchJoin[] { orderSearchJoin };
    SearchResult response = netSuiteService.search(searchParts);
    return response;
}