Translating German Driving License at JAF

Hello everyone, I have a German driving license and last days I was in Japan for work. I booked a three-day vacation in Okinawa after but because I’ve been busy, I didn’t have time to check the requirements for driving here. When booking the rental, I asked if my debit card and German license were enough, and they said the credit card was required, but didn’t mention the international driving permit (IDP). When I arrived in Okinawa, both the rental office and I were surprised that I didn’t have an IDP. As a solution, they suggested I contact JAF. I sent an application late evening (afternoon in Germany) and got a response within 5 minutes:

„Thank you for your message. Your application is already being processed and will be finished and ready for print-out tomorrow morning.

Please note that the final signed documents are issued by the Japan Automobile Federation, whose working hours are from 9:00 AM to 5:00 PM JST. Unfortunately, it’s not possible to issue a new driver's license translation outside of these hours.“

From what I understand, this is processed on the German side. I have already planned itinerary with a car and payed 44.90€ for the translation. I am getting really stressed and my questions are:
1) Do I need any additional checks or paperwork from the Japanese side?
2) Can I expect to get the IDP as soon as the Japanese office opens?
3) There is also one JAF office in the city, should I wait e-mail or go there directly?

Thanks in advance for any guidance!

by Former-Lock-6856