For example, what if I embed the invoice data in a JSON file in a PDF? Could that make it easier for the user?
I really don't know much about PDF, but from what little I just read after checking it is possible to do that.
Here is a python lib that does it: https://pypi.org/project/factur-x/
Odoo, an open source invoicing software, produces factur-x invoices systematically (whatever the country): very convenient as it's parsed automatically.
Another benefit is that it's really easy to recognize an invoice at a glance, and you know exactly where all the info is.
[1] https://en.wikipedia.org/wiki/Universal_Business_Language
If you have access to a large number of vendors (invoice templates), these templates are going to be really valuable for creating better models. If you provide samples as a free/open dataset, you could make all invoice models that use your dataset, even if developed by other companies, better on your distribution.