Isnt point floor loading an issue here with the weight of the truck and load being passed through the hard polyurethane laod wheels which don't give in the same way rubber does. Its probably 6 tonnes over, 6 sq ins per wheel? Many years ago I saw a reach truck go through a container floor but perhaps shipping containers are stronger today than they were 20 years ago?

Should not be a problem - used the NYK (Nichiyu) brand mast reach in the states for the same purpose. Used 4.8 meter full free lift triple mast w/side shift. Loads were stacked two high (approx 600 mm high on 600 mm x 500 mm pallet.
Two areas of concern you need to check out closely:
1. Will all the container door opening heights be the same - they can vary & cause you issues if the lowered height of the mast or OHG is too high.
2. Compare the maximum break over angle (between front & rear tires at the lowest point of the reach truck to the maximum break over angle of dock plate at the lowest & highest point. To make certain the reach truck will not get hyng up when either entering or exiting the container. Most mast reach trucks have approx 75mm of underclearnance