I assume you are a host, and ordinarily we come to folks like you for answers to these questions
That's not very reassuring, I wanted to use Soho so my clients could have reasonably advanced websites and not have to pay heaps in support. I'm not seeing much value so far. I spend more time debugging client problems that are illogical and the one test client is becoming very frustrated.
Given that the error defies common systems logic I suspected that it would be a problem that Soho would be used to dealing with by now. How can a program generate files that fail to write to directories with 777 permissions then? The application must be checking something other than permission, yet it returns a permissions error. If the fault is Apache, then the error message should say so.
I turned ModSecurity off temporarily in all the .htaccess files (it's on again now) and at last that allowed the upgrade to happen. Not too sure how I feel about giving those instructions to a dog breeder but he's reasonably brave, hence his being selected as the Guinea Pig.
Now all we have to do is see if that is the same thing that's blocking his access to image changes, adding new code and the recent failure of the form captcha.