Haven't heard about the dishwasher detergent but I use simple green. It cuts through the suntan oils pretty well and does not produce a lot of suds. Plus, I think it is much cheaper then dishwasher detergent and I can use the leftovers to wash the deck and patio.

First I spray down the cartridges to remove most of the dirt and then I soak them overnight in a large garbage can with simple green. A quick spray down again and reinstall.