A lot of people cover their screen tops with Plexiglass. Just make as many holes as you need to get the desired humidity. Start with fewer holes and if the humidity is too high then make more holes.

Your heat lamps are causing the low humidity. If you can get rid of those then your humidity will shoot right up. That being said, your temps are more important than the humidity. If you can get the humidity up temporarily during the shed cycle then you should be just fine.

A tub would also be a simple and cheap solution :-)

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