So I bought a huge light for my zen habitat. Really over kill. I had originally had it in the tank strapped to the top, but had noticed that he was squinting a lot so decided to put it on top of the screen. I know this is a powerful light, but is putting it on the screen going to make it too weak?
It should be OK as long as you provide areas to climb that allow close access to the light if he wants it. Through the screen top you'll probably want it to be 10-12'' or so above the main basking area.
How close was the light before you moved it? He may have been closing his eyes while basking as relaxation rather than irritation. If the light is shining from directly overhead rather than at an angle, it isn't likely to cause a problem for them. Without the screen blocking the UVB, that light is best at around 12-14'' or so above the main basking area.
16'' is a bit far, especially if it's on top of the screen. For a T5 like that I'd say no closer than 7 or 8'' but the ideal output (3-6 UVI) tends to be around 12-14'' with those bulbs. When you have it on the screen, that intercepts some of the UVB and the 3-6 UVI range becomes closer to about 10-12'' or so, roughly.
I just measured the output from my T5 (Arcadia 12%) at 16'' and it is 2.5 UVI which isn't bad, but you'd want to offer some areas with a bit more for basking, which is why the 12-14'' range is recommended.