Thanks!
Okay, so the main reason that did not work was, because that is an object storage field, and those are not supported officially – only text based fields. ACF does not return the field choices for those types of fields.
However, you have added FTP access, so I have tried to make a direct modification to somehow fetch those post object. It seems that there are a lot more values within that drop-down now, but I can not guarantee it will work for all of the cases.