Hello,
Well, you are right, the screen does filter out quite a lot of UVB. Can you possibly mount the fixture with the tube bulb directly underneath the screen top lid with wire ties or something? Does the fixture that you bought have reflective backing? If so, that does almost double the UVB emissions of your tube bulb.
I am happy that you decided to stop using the compact or coil bulb. Unfortunately they are very dangerous, & do not have very good UVB emissions.
Tracie