I would find a way to hang the lamp. Also, if they aren't leaving and you haven't any animals which will get them, there's no reason you couldn't have a gap.
Remember, melting or softened plastic releases toxic gases, and birds are far more susceptible to them than humans- be very careful with the heat and plastic.
I have a clamp light that is clamped to a bathroom cupboard and angled at my kids, but the temp is very warm some times of day, and I then move the cupboard farther away...close it some. Very unscientific, but it works. You might try hanging your lamp on a coat rack, or over plant hook if that will give you a greater distance to cooler temps.
** Edited to add_
-Also, I think I have the same bulb- mines at an angle, pointed at the far side of my rubbermaid tub (green tub) across the airspace of the tub, and the distance is 28" from front of bulb to far side of tub. Granted my chicks are 1 1/2 to 2 1/2 weeks old in that tub, but it keeps the ambient air temp at 85 F. The bulb is just 8" above the near side, angled down at far side.