Redoing pillars on lug cabin,

This post is similar to Cameron's  post but I have few more questions . I will have to redo the pillars of an old lug cabin. The actual pillars have the same layout as Cameron's. The outer pillars on each side of the cabin sank 2'' outward. This lug cabin is 16'x16'  built on pillars of 6''x6'' square lug resting on 24''x24''x2'' patio plates. Over time, they sank because(my guess was that the weight of the cabin is resting on the very edge of the patio plate) causing the floor to be 2''in the middle compare to the sides of the cabin. So my work will be raising the cabin back 2'', building bigger plates.
1)  The top soil of the land is sand and very deep. To do the ground work, what material should I use and compact under the base, and how much, in order to limit the ground movement due to frost?
2) the size of the new bases and how thick ? Reinforced or not ?

Now, comes to raising the cabin, I plan on using (2) 20t jacks, do one side and than, the other side. Is there a risk to damage the chinking? Any suggestions?

Thank you.