Lots of new chick people think the brooder has to be all nice and uniformly warm, like an oven, and that's why the chicks may be having a problem with the heat. They have no cool zones to cool off.
The heat guidelines are helpful and it would be even more helpful if it pointed out that the recommended temps are measured directly beneath the heat source only, and the rest of the brooder must be much cooler!
As has already been suggested, a much lower wattage bulb, 100 or even 60 watts, might be adequate. It's a shame they sell only those 250 watt bulbs with the chicks when they're more suited to keeping food hot.
I suggest the heating pad system for greater chick comfort and less heat related problems.
Also, you can rig up a brooding pen outdoors easily, either in your run or in the coop, regardless of adult chickens. See my article linked below in my signature line. Baby chicks benefit greatly from much cooler ambient temps as well as having a much larger space in which to grow and develop.