I wonder if you could use tubes instead of just holes drilled in the box. My thinking is that perhaps the anemone can feel that it’s open on the other side and climbs through. If the tubes are say an inch long maybe they won’t feel that it’s open on the other side? Flow going into the box would need to be very directional though; parallel with the tubes.
I believe that one of the reasons they move around in boxes is simply because they don't feel safe. Nems like to have a firm anchor either deep into sand or deep into a crevice (depending on species.) In a box they never get that firm anchor.