They might be able to climb that, but only the nymphs around 1/2" and under. I would do like diggerdrake suggested and line the very top of the container with clear packing tape just to be on the safe side. Hard to tell how smooth those sides are and they can climb some of the colored containers. I had my nice new tote setup for them and dumped them in as soon as they came in. The babies when crawling up the sides promptly and I played crowd control then.
As far as the eggcrates being too close to the top, no big deal there if you are going to use a lid. If you are not going to use a lid, then be warned that the adult males have the ability to hop and flutter a small amount. They can maybe get 3-4" max vertically, so I would make sure the crates are below that threshold if you don't have a lid on the container.