"Mabel did not come forward with her story until 1990, and some of her recollections are not consistent with the historical record".
I'm not so sure they were incapable of doing work based on what someone remembered 53 years later. It is not known when Betty's description of injuries was made. It could have been on the 5th Day. Fred "complained of his head" could simply be a headache or dehydration on the 5th day.
The water supply may have been limited but from the Radio messages they lived for 5 days minimum?
Maybe they did the work on the 3rd day when they still had strength. I don't think we should underestimate that they could have used enginuity to get work done with limited effort. A lightweight pole could lever up 3000 lbs. or they simply found an actual jack on the ship. Anyway that was just one explaination. They could simply have drove up to a high point and staked it down. I was just offering a few possibilities to explain how high up the wheel in the image looks. Of course assuming it is a wheel right side up. One image I saw looked like the wheel was upside down.