IMO, I maintain that the 'pressing screen' has been mis-named.... if you fold it over on top of the hash, and press down or dab it at all, you are pressing the wet hash, and rupturing some heads. This makes it real sticky and hard to chop up on the cardboard.
I think it should be renamed the dabbing screen... try this:
Place the dabbing screen on top of several layers of paper towel. Scoop your wet hash out of the bags, and just plop it on top of the dabbing screen. Rinse the spoon in the next bag. Repeat for each bag. Enough water will wick out of the hash into the paper towel thru the screen, without rupturing any heads. The hash is then the consistency of wet sand, and you can more easily feather it apart rather than chop it up, and less sticks to the cardboard and knife. The wet sandy blobs are easier to put thru a sieve screen as well if you are going that way.
Just my personal technique, if it works for you, great. If you happen to come up with something better, please post it
YBG