FedEx "Eligibility for issuance of US Security Clearance" could be an issue if you're South African and fresh off the plane. If you go for FedEx, make sure the US authorities will be able to check your background to their satisfaction.
An idea: If you meet all the FAA requirements, and not the US residence requirements, but can get European residence, can you fly N-registered European-based aircraft for FedEx (or maybe UPS)? Mind you, then the suggestion to meet the EASA requirements and then get a job with the orange mob seems like a good idea.