It seems that containers may be too heavy. The most powerful chopper (the M-26) lifts up to 20,000kg (with most heavy-lift choppers probably lifting about half that), while some containers may wel exceed 30,000kg.
That is 56.8 to 62.5 tons, depending on the type of ton. Lift two containers at once.
Making things even easier, the shipping company knows the position and weight of every container. The containers have been carefully placed, keeping the weight low and spread evenly. The containers on top are the low-weight ones.
You're right that most of the heaviest containers would be at the bottom of the stack. That's kind of a mixed blessing though..
Depending on the temperature as the site, that could be a lot lower.