Yes, cover your screen top with aluminum foil or damp towels. Just leave a space for some air exchange and for your heat lamps. I would also switch to cypress mulch, eco earth, coco fibers, or a mixture of them all as your substrate instead of aspen. These will help to lock in moisture. You will need to moist the enclosure at least twice a day.

I'm sorry to say this, but you will battle humidity all day, every day. Tanks just don't hold humidity well at all. You can make it work, but it will take a lot of time and dedication.