Have you looked into the possibility of a South African doctoral program? The primary South African DL university is UNISA (University of South Africa), from which I earned a BA(Hons) degree a number of years ago. They are a very large university with international recognition but are also (in)famous for their multi-layered bureaucracy. Even with the difficulties in receiving responses from the school, UNISA is an excellent value - you are getting a very solid, mid-level quality RA-equivalent for the cost of
a community college!
UNISA homepage
While UNISA is 100% DL (though they have study centres in various locations in SA and Namibia), B&M SA universities also have provisions for "part-time" doctoral studies in various disciplines. This "part-time" study is essentially distance learning. At the doctoral level in SA (including UNISA) there is no formal coursework but rather a thesis(dissertation) proposal, the thesis(dissertation) itself and the oral defense.
Four additional points:
1) Due to a reorganization and consolidation of the SA university system, many schools focused their specializations in several areas. Hence, perhaps only a handful will offer the program you want.
2) Check how frequently you will have to go to SA. With UNISA you can probably get away with a single visit to defend you thesis*(dissertation) but that may not be the case with all programs.
3) Jack Tracey of DegreeDiscussion was accepted into and enrolled in a PhD program at University of the Free State. He is usually generous with his time and in providing info if you ask.
4) You can find a lot of useful info on UNISA at degreeinfo. Look for posts by Brad Sweet as he actually has a UNISA PhD; ignore anything written by Chip (the owner) as he doesn't know what he's talking about.
* UNISA's Graduate School of Business Leadership offers a Doctor of Business Leadership (DBL) that while 100% DL, also require that you attend several "colloquia" while a dcotoral student. That translates into 4 visits to SA plus yout oral defense.