Binder clips and fleece can work brilliantly. Lots of bargain shops have fleece blankets for £1. You can fold them, cut them, do whatever you like with them.....then clip it on to your grids. A favourite is making a triangle then clipping that into a corner - kind of making a roof for them.
Another thing is the car wash idea. Fitting a grid to a corner like a roof, then tying lots of strips of thinly cut fleece, so that they hang down looking like a car wash. Make sure the fleece doesn't drag on the floor though....it can get a bit smelly otherwise. You could even place a bit of fleece over the to of the grid to give it a roof!
Fleece and clips.....the limit is your imagination! Lol