The screen and plexi are not allowing the beneficial UV rays to penetrate.
I would cut out holes for the lights and move them to the center of the aquarium. I would also give the baby two hiding places or some plastic plants to hide under. It's probably pretty stressful for the little one to not be able to get away from the glaring light. That might be why he 'sleeps all the time.'
You'd have to cut holes in the screen as well as in the plexiglass.
It shouldn't cause a fire but then again I'm not sure what your substrate is.
I think coco coir is mainly used for hatchlings as it holds humidity really well. But it shouldn't catch on fire either.
You're not putting the bulb on top of the substrate, you're still leaving it at the height it's at, just removing the two layers between it.
I think I read your post too fast. You meant leaving a gap for the lights and leaving the plexiglass around the rest of the areas?
That would be fine, but your lights should be in the center of your tank, so some plexiglass cutting would likely have to happen anyway.
Also, leaving gaps at the top will allow your humidity to escape so you still might have issues keeping the % up.
I would cut the lamp size instead of leaving gaps.