Simfan made a suggestion, but I don't think it got much feedback:
Number 7 is slightly problematic as we have no control over what is appropriate for a "doctoral-level" degree. That could become a rather large loophole if we leave it that way.
I had had similar thoughts about this, and I do think the term a "locally accredited, non-profit degree-granting academic institution" might cover the issue well.
Sounds okay to me, but I don't really know what the other options are. Is there some sort of international accreditation process that would be a better fit? The UN's
International Association of Universities falls incredibly short.