Ken and Dave -
Thanks for posting all the math. A few comments - As a historian researching ice cellars and ice houses, I've learned that once you dig past a meter or so, the year round soil temperature in central New England is around 50F. So, huge amounts of work do dig a pit or cellar, without huge benefit. Prior to 1805 it was all cellars (Washington at Mount Vernon, Jefferson at White House and Monticello), but after Frederic Tudor commercialized the process of storing and shipping ice it was all in above ground buildings - initially brick or stone, but then wood.
For the cellars, before filling, bottom filled with a foot of gravel and two feet of sawdust on top of that (packed to less then a foot once ice added). Then planked first or ice directly on top of sawdust. As filled, a gap of one foot left between walls and ice, to be filled with packed down sawdust. Or, an inner wood wall built and the space between the wood wall and the outer stone-lined pit wall filled with sawdust.
A common design for small ice houses was a double-walled wood building 10-20 feet wide (all inside dimensions), 10-15 feet high, and 15-30 feet long. If you look up ice house and Tobyhanna, PA, they have an ice house that holds 50-60 tons, and is filled every winter. The gap between the inside and outside walls about one foot, filled with sawdust.
I've seen mention of Amish using expanded polystyrene block 18-24 inches thick (about r=5 per inch). Have to allow for drainage at bottom and venting at top so that any warmer air can escape.