Hello cleegus.
I live in SA and love walking, but it really is hot and dry in summer. The locals mostly frequent beaches at that time of year.
Unless you are used to it, and know the area well, I suspect the combination of hot and dry could be very dangerous.
I have never done an overnight walk in summer in SA. We did do an overnight walk in the Lower Flinders [Alligator Gorge] on 30th Oct a few years back. It was the last day when overnight hiking was allowed, and it was a long and hot walk. No troubles with water due to tanks and dams along the way - but very taxing with heat. Summer is potentially a lot worse than we experienced then.
We also did a few hours walk in Nov at Wilpena Pound (middle Flinders) and despite starting early we all "melted" for this short walk. Most spent the rest of the day in a swimming pool at the resort.
The Victor Harbor area is generally cooler - even on hot days. Proximity to the ocean is key. But water supply is always the chief concern.
I have carried up to 8 litres at a time - but that was walking in winter. Then it lasted 3 days - but it would last a lot less time in summer.
If it is primarily solitude you are after - you might get it by camping next to a car at Waitpinga Beach [which is on the Heysen Trail].
Depending on when you go - SA can be a quiet place. Not a lot of crowds.
Having said that - there is a walkers hut in Deep Creek [Eagle Waterhole] - check the pamphlet photohiker mentions. It would probably be the one place I might contemplate an overnighter with its adjacent water tank. However, the distances are not great - it is an easy walk to cross the park in a day. But you could work it into a nice loop as my son and a friend did. You would still need to check with the rangers that an overnighter is allowed, but I cannot see anything stopping this. It would definitely be closed though on days declared as Extreme Fire Danger.
Note that the pamphlet says:
"Carry sufficient food and drinking water. • Allow 4 litres of water per person per day.
Do not rely on tanks or creeks in the park for drinking water."
It will be no open fires throughout the year, but I think you would need to plan on no fire at all now that fire ban season has started.
For overnight treks in summer - we go to Tasmania

But I am about to try the real alpine parts of NSW/Vic next week.