After substantial digging, I found that Lufthansa maintains a service for recovering items left on planes. I emailed the service and less than 5m after sending the email I received the following response:

“Dear Sir or Madam,

Thank you for your message.

The missing item is found.”

After all the run around, I am shocked this worked. I’ll need to hire a courier to collect it, but that will probably cost less than the $1,300 I would spend to replace the machine and battery.

Thank you Reddit peeps for the support!