Ancestry Visa - South African Birth Certificate Error/ Can I still apply?

Hi - long one sorry! But I'm VERY desperate & would appreciate any help!
I am originally from Zimbabwe, and my mother changed my surname from my father's to her maiden name.
So I am now applying for my ancestry visa through my father - I had to get a South African birth certificate that had his name as my father but with my new surname.
After 6 months of calling Home Affairs weekly about my birth certificate, it finally arrived.

However, my father's birth year is incorrect (1979 instead of 1974) & Home Affairs are reluctant to correct it as my father is not in South Africa.

Is there any way I can go around this?
Would an affidavit from my father stating that the information is incorrect on my South African birth certificate but he is the father & would be willing to take a DNA test? (DNA is very pricey)

I have my original Zimbabwean Birth Certificate - but my surname has changed - that is why I needed a South African one

I have job offers in the UK & can't afford to wait another 6 months for the correction.