As a South African travelling to South Africa and returning to live in UK on a BRP what passport validity do I need

My family are travelling to South Africa on 30 Mar 2022, returning on 23 Apr 2022. We live in the UK with BRPs (4 years so far). We only have South African passports, not British Citizenship yet (or ILR). We have effectively immigrated to UK, this is where we live and work.

My daughter's passport expires on 6 Aug 2022. I have applied for a new one (Sep 2021), but the current estimates are 1 year to receive it, so it won't arrive in time.

When we leave for South Africa, it will have ~4 months validity remaining and when we return to UK it will have over 3 months remaining.

What validity do we need remaining on her passport to be able to travel?

I have called UK immigration. They can't answer the question, they've directed me to the South African embassy and I can't get hold of them at all. I have tried contacting SA Dept of Home Affairs and asked various groups for advice, but so far no definitive answer.

The best source of information I've found so far are SA DHA indicating that South Africa will allow you to travel with 30 days remaining on your passport, so I think entry to SA should be fine (http://www.dha.gov.za/index.php/travel-documents2)

However, I can't determine what is an acceptable validity for returning to UK on South African passports with BRPs. The best I've found is information on gov.uk indicating that UK requires a passport valid for the whole of your stay (https://www.gov.uk/uk-border-control/before-you-leave-for-the-uk). It isn't possible, we have immigrated, we have valid BRPs, but we don't have British passports yet, and we can't have SA passports with indefinite validity.