Hi Sascha,
I'm sorry for taking your time to give further information, but since I don't have access to source codes and can't check them myself, I wanted to make sure that everything is just as I expected.
Thanks for the screenshots. There are last two questions I wanted to ask about the BAdI and then I'm suggesting another solution. But first let's make sure about the BAdI first:
1 - In ORDER_SAVE BAdI, in which method you wrote your code? I hope it's CHANGE_BEFORE_UPDATE.
2- If you have your codes in CHANGE_BEFORE_UPDATE and all the other methods are either empty or just working fine, would you mind share the codes in all methods of that BAdI? If it's not appropriate to share it here, you can send it to em via private message.
If we even can't make out after we try these two questions, I'll suggest you to use action profile for adding marketing permissions. If you're already experienced in action in transactions, you just need to adjust schedule/start conditions according to your requirements. If you're not experienced with actions and action profiles, I can share some documents to assist you
Best Regards,