You can easily cut down the 20ppi blue foams to half height by dampenening them (damp not soaked) and then freezing them for a couple of hours. The frozen foam will stand up to some pressure so now you can cut it with a large and sharp unserrated knife such as a Japanese Yanagiba.
I originally thought that a bread knife might be good to cut filter foam as both substances have a similar internal structure. Unfortunately it seemed to catch teeth at every opportunity. Similarly I did not have good results with trying to use hacksaws or other saws.