Lexmark and other MFP Printer manufacturers allow developers to create Apps for their devices.

We can create an MFP Printer App for Lexmark printers that could hold a copy of our PDFs. In an Offline/Downtime event, those PDFs could be selected (with the number of copies) and printed directly from the printer.

For Lexmark:
To get access to the eSF SDK for embedded Java apps that run directly on the MFP, you'll need to contact Lexmark Professional Services or become a qualified partner through their partner program.

HP:
HP Workpath SDK available through developers.hp.com

Ricoh:
Ricoh Developer Program allows for access to their SmartSDK / Embedded Software Architecture.

NOTE:
Because these are blank forms, you do not need to worry about PHI access.
If we wanted that, it is possible but requires the customer have badge access setup on the printer.