The original template (still in the addons) showed:
<p><b>Order:</b> <perch:shop id="orderInvoiceNumber" type="hidden" /></p>
But nothing was being shown. I dropped a showall on the template and could see anything whatsoever to do with invoice number?
It seems to correlate with order ID, so Im not sure why it's separate, but hopefully the client will be able to manage.