Below are two insert statements that return an error: "There is a missing element: TxnID" These inserts work fine on a different QB database file ... what gives? 

INSERT INTO InvoiceLine (CustomerRefFullName, ClassRefFullName, TemplateRefFullName, BillAddressAddr1, BillAddressAddr2, BillAddressCity, BillAddressState, BillAddressCountry, ShipDate, InvoiceLineItemRefFullName, InvoiceLineDesc, InvoiceLineQuantity, InvoiceLineSalesTaxCodeRefFullName, FQSaveToCache, CustomFieldreferral) VALUES ('Abbas Aida', 'Class Name', 'DMK Medical PLLC', '', '', '', '', '', {d'2006-06-29'}, 'Procedures Facial:Platysmaplasty - Short Flap', 'Platysmaplasty - Short Flap', 1, 'Non', 1, '17')

INSERT INTO InvoiceLine (CustomerRefFullName, ClassRefFullName, TemplateRefFullName, BillAddressAddr1, BillAddressAddr2, BillAddressCity, BillAddressState, BillAddressCountry, ShipDate, InvoiceLineItemRefFullName, InvoiceLineDesc, InvoiceLineQuantity, InvoiceLineSalesTaxCodeRefFullName, FQSaveToCache, CustomFieldreferral) VALUES ('Abbas Aida', 'Class Name', 'DMK Medical PLLC', '', '', '', '', '', {d'2006-06-29'}, 'Procedures Facial:Lifestyle Lift', 'Lifestyle Lift', 1, 'Non', 0, '17')

I suggest you turn on the trace log and see what the actual error is. Most likely one of the FullName references isn't valid for the company file you're working with.

See: How do I turn on the trace log? 

You should also check if there's a difference in your Use Case Sensitive RefNumber Searches setting.

Use Case Sensitive RefNumber Searches when checked means a refnumber of 'ABC' and 'abc' will be different, but means QuickBooks can use an index internally for a search instead of a complete table scan. (Note: this feature applies to versions of QuickBooks 2005 and higher)