European Professional Doctorate

[Tomas]

My needs for the study is merely knowledge gaps and research practice, so I don’t care much about accreditations or whether it’s a Titulo Propio certificate, as long as the institution has some legal incorporation and/or granting power to have some assurance of program quality.

Not sure what you mean by "some legal incorporation", also not caring about accreditations yet wanting some assurance of program quality seems a bit contradictory to me.
CIE is legally incorporated as a limited liability company. I'm almost sure there is nothing that could be named "granting power" with them, I even doubt presence of any assurance of program quality.  Basically it's a business selling courses on anything they can that doesn't require accreditation in Czech. People behind it have connection to FVES (Czech "branch" of Jagiellonian College in Toruń), maybe that's where most of their degrees are from.
Collegium Humanum at least is a private university (which doesn't mean their degrees like LLD LLM are accredited, I'd bet they are offering it as professional education).