Louise and I bring frozen 2-liter bottles of water and/or gallon milk jugs frozen at home. We do the 2-cooler dance, and we generally run out of ice Friday or Saturday. We plan on that and generally don't buy ice while we're at BM.
However, in the interests of learning, I was contemplating buying a honkin' huge cooler and stocking it with block ice, as a sales person told me block ice would last all week, where dry ice will keep stuff frozen a day or two then disappear (which, by the way, has been my experience with the 2-cooler situation). I was hoping the huge cooler with blocks of ice would last from Sunday to Tuesday or so, which is when we plan on being on the playa (we volunteer, so we get an extended stay of about 10 days with permission).
The thread on dry ice has lots of information, but our current coolers don't seem big enough to contain all the tons of dry ice people report buying. We can squeeze a block or two in our reserve cooler, but not 20 or 40 lbs.
Since nobody has information on how long blocks last, we'll just keep on doing it the way we have been.