How wet/damp are the egg trays?
The sharp smell you smelling would be urine mixed with moisture and the poo.
The nice thing about the non climbing species, you can leave the lid off and only put it back on at night.
I use lace curtain and wire mesh to seal off the lid on my container.
The lace curtain works the best with stopping the nymphs from climbing through.
So here are some photo's of how I do it.
Metal
The mesh is just there for extra escape proof, but the roaches can climb on it once the lid is on.
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Lace
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Mixture of lace and metal.
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Vasiline "lip"
You have to redo the "lip" every so often or the roaches start climbing.
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Not really, I have a feeding container that I feed from that has a vasiline lip around it, the container can stand open the whole process of feeding and you don't have to worry about the roaches escaping.
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How I deal with moisture issues.
I put some egg tray flat, with some peat under it, then I flood them with water.
I also mist the top of the egg trays.
Just until there is enough mess at the bottom of the container then I flood the bottom directly, this also helps with hatching of the nymphs and giving them humidity.
Bearing in mind that can get very stinky so if it is in your house don't do it, mine is in the outside room.
I also use leaves, that has been soaked in water.
But when the urine smell becomes to strong I clean out, with new trays, to start the process over again!