After much experimentation I have found one method to make big clear chunks of ice. That method is to put water in a cooler in the freezer, then chop off the top clear layer. Now the trick was to get this into useful sized cubes for glasses.
*Update 2021: A better post on cutting up clear ice is here.
Starting with the slab of ice (this one about three inches thick),
I used a heated bread knife to score the ice just about 1/8th of an inch,
Then tapped the scratch in several places with an ice pick and found it separated really easily.
And I got the whole thing chopped into long spears.
I use these really long ones in a tall glass
and scored and cut the rest of the spears into big fat cubes.
Hooray! Time for a drink.
An index of all of the ice experiments on Alcademics can be found here.