so, i installed a clone of your site here and made 3 orders
1 COD, 1 Paypal and another Paypal order with the unedited version of the postcode plugin (v4.0.30)
in all 3 cases did i get the plz in my emails and order history in the expected places.
as i left the cloudprint plugin enabled and pointing at your printer, i also suspect you got those 3 orders printed out on your printer with also all the plz’s printed as expected (??)