Adelaide to Alice Springs is all tarmac and relatively easy, particularly if you’re not in a hurry. I did this in August 2018 along with others. I notice that the last checkin on PlugShare for Glendambo, Marla, Kulgera and Erldunda are in March so they should be functioning still. All of the named charge stops have a 32A 3 phase power point readily available. The only proviso is Kulgera as the power point is normally in use for the car lift and if the owner is using it or not there you have to fall back on 15A single phase campsite charging.
I would not travel this route without a spare, jack and tools to change a tyre and if you’re a member of TOCA you may be able to borrow a spare wheel and some charging or extension cables.
My itinerary was Adelaide, Clare Valley Supercharger, Port Augusta Majestic Oasis Hotel on day 1.
Port Augusta to Glendambo Road House then Coober Pedy Desert Cave Hotel day 2
Coober Pedy Marla Road House and overnight in Kulgera On 15A campsite day 3
If I did it again I would charge longer at Marla to get to Earldunda.
Day 4 Kulgera to Alice.
If you only have one mobile phone, make it an Optus phone as some towns are Telstra Only that the car works on and some are Optus only and then you can connect the car to the Optus phone to plan the next leg.
I didn’t do Kings Canyon and or Uluru so I’ll leave that part for others.
Whilst the route is regularly trafficked by Grey Nomads who will often stop to help if you’re in trouble this is a seriously remote location and should be respected as such. There are online guides like this
Stuart Highway Facts - Explorer's Way from Adelaide to Alice Springs
Good luck.
P.S. When charging during the day for the next leg, put in the Next charge destination into navigation and it will tell you that you will have minus X percent when you arrive, as you charge this will go down to zero then I would leave when it told me I would have 10% to 15% at the next charge stop.