After a car crash leaves him unable to walk and dying of thirst, an inventor and his physically-disabled cousin must traverse the harsh Australian desert using only her electric wheelchair.

I think the re drafts of the logline work well.

Perhaps, as DPG suggested, add in a time frame and mention how far out from the nearest town they crashed.

For example:

After his legs are crushed in an accident, 3 days out from the nearest town, an inventor and his physically-disabled cousin must use her electric wheelchair to escape the harsh Australian desert before dying of thirst.

Agreed about the wheel chair, it is an original addition to the survival tale.
Most survival plots are about a perfectly fit person who deteriorates over time in their exposure to the elements and lack of resources, only through their tenacity do they figure out ways to survive the harsh conditions.

In this instance you introduced an element that starts the survival off with a handy-cap, this means the obstacle is even greater to overcome.

One thing though, in most successful survival plots there is a personal element that motivates the main character to defy the odds and survive.? It was the girlfriend in Cast Away, revenge for his son in The Revenant and visions of his child to be in 127 Hours, what personal element can you add to this as a motivation for the main character?

Also I believe if the inventor him self was wheel chair bound and he had to survive on his own the stakes would be even greater. Having one able body between them means he could walk ahead and get help, but on his own he has to invent in-order to survive or else.

Secondly the placement of “…dying of thirst…” is confusing, as the car accident didn’t make them die of thirst rather the conditions did, perhaps change it to:
After a car crash in the Australian outback a disabled inventor must engineer the worlds most efficient solar panel in-order to trek back to civilization before he dies of thirst using nothing but his electric wheel chair.