What you are looking for is either a validation based o your SA license or a conversion to a standalone FAA certificate.
Validation is in accordance with 61.75
Electronic Code of Federal Regulations: This can only be done in the USA. Process is free, just takes some time.
And no you cannot get a CPL this way, PPL with additional ratings only like IR or ME.
For a standalone FAA certificate you will need to come to the US for training and a check ride. This requires a M-1 visa.
But your situation is a little more complex.
to do some voluntary humanitarian work in an N-reg aircraft.
I'm 99% sure that this will require a CPL.
Do the Tanzania Aviation Authorities allow you to fly a N-reg on a Tanzania License? The US doesn't care what certificate you hold flying an N-reg outside of the US, unless the operator requires a FAA Ticket You have to abide by the laws of the country you are flying in. It may be a whole lot quicker to arrange a Tanzania CPL.
What is it MAF?