The thing is that I'm not a US citizen, so if I go the US route and finish the training there I will be holding an FAA license with no right to work on N-reg aircraft.
Not true. You won't be able to work in US but not being an US citizen does not prevent you from flying N-reg somewhere else in the world.
I can understand the way you think because I was in your shoes few years back. I'm neither American nor South African. I've got my CPL initially from South Africa. SA CPL hasn't helped me much in regards to getting a job so I converted SA CPL to FAA CPL which got me a job on N-reg in Africa. Its all gonna be about luck and lot of networking after you finish your training regardless of license you gonna posses. So I guess you won't make a mistake either way you go. If you want to concentrate on African market after getting your CPL, maybe doing your training in South Africa would be a better choice and as Digitalsoul said, much easier in regards to student visa and other formalities. Also the aviation in SA is great and quality of flight training is excellent.
After that, you can always go to US and get an FAA license. It took me a week to get FAA CPL.