Hello and welcome back at Wefugees!
The "Orientierungskurs" is part of the broader integration course and focuses on providing knowledge about German society, including its legal system, culture, and values.
The "Einbürgerungstest" (exam for the naturalization) contains almost the same questions as the so-called "Leben in Deutschland" exam (which is the most common certificate to prove the required "basic knowledge of the legal and social system and living conditions in Germany"). Therefore, the immigration office should accept this as well. However, I learned about some cases in which the civil servants at the immigration office were persistently asking for the "Leben in Deutschland" test. I recommend to give it a try nevertheless if you can manage to get an appointment for this earlier.
Otherwise you may explain to the immigration office that you can not get any appointment within their deadline (with presenting your booked appointment for the later date) and ask for an extension. In case you face difficulties, I recommend to get support at a migration counselling office.
I hope this helps and good luck!
Regards,
Meike