This information is available by default in both Customer Invoices and Vendor Invoices for all Quicken for Windows H&B and/or RPM
Here's a portion of the data entry form from my Q 2018 HB&R
You're right as far as printing the Project/Job number on the paper invoice is concerned. That is not available at this time.I support your idea about having this item added to the Invoice Forms Designer so that it can be printed.
The Memo field does not print on the paper invoice either and should be added.
Until the programmers make this change in a future release of Quicken, as a workaround I recommend you continue to use a dummy line item description or use the Message to Customer field.
The P.O. Number field is available for printing, however.Please review the customization of your Invoice form in the Forms Designer and make sure this item is enabled for printing.