OK I know that can't climb much, but I'm worried about them being able to climb the little distance I have in the sterilite's I got. The tubs are 35gal tubs- I'm setting up 2 and will have ~1k in each. My question is- with how little room there is from the tops of the egg flats to the top of the tub- should I put on some vaseline to play it safe for escapees?
clear package tape works well too. the roaches should not be able to climb as long as the inside surface is very smooth. even with a little texture the only ones that can climb would be the small nymphs and then they will slip off as they dont have good traction. but the roaches will most likely hang out in the egg flats and do their thing. why try to escape when you get fed well and plenty of water. they are oblivious to their final destination and would rather hang out and colonize with the others in a nice warm dark area.
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.