To move one took a Caterpillar about the size of a D-8 or larger. We had a TD-25 on the property moving stumps and that got the job done more quickly. The D-8 was fun to drive compared to all the lever pulling and gear shifting on my antique D-2 Caterpillar.
All the Kamado style cookers I have had have all been a manual affair and that was one of the things I enjoyed about it. Like cooking on a wood fired cookrange, it took paying attention to the fire, and therefore slowed you down from the frenetic pace of modern life.