This may refer to two possible churches:
The African Apostolic Church of John Maranke was founded by John Maranke (1913-1963), a former Methodist from the Umtali area (where Godwin lived). In July 1932 he was called in a vision to be Christ's apostle. He spent the next thirty years travelling on foot around Southern Africa, converting and baptising thousands of people. By 1996, the movement had exceeded one million followers.
The African Apostolic Church was founded by Paul Mwazha a little further to the west - but not until 1957, so the timing may be a bit tight. However, an important clue is Godwin's description of the men shaving their heads and growing long beards - the look Mr Mwazha and his followers sport in this video:
There are more than 10,000 African Initiated Churches in South Africa alone, so it is unsurprising that two indigenous Zimbabwean churches share this name.