What you need to do is get fiberglass mat and cut it into like 1"x2" squares, dip it in the fiberglass resin, and then lay it inside brushing the resin on nice and uniform.
Yea reinforcing it with fiberglass is a very good idea, and highly recommended for Fett helmets that are resin, though its not 100% needed if you are aware of the warping issue and store your helmet away from extreme heat.
However, you dont dip the glass in the resin,that makes a huge mess and is not the proper way to do that. You can also cut the glass pieces a little larger than 1"X2". When i do helmets, i use pieces about 2"X6", but either will work.
The proper way to do it, is to brush some of the polyester fiberglass resin on the inside of the helmet, like paint basically, uniformly , and in the general area you will lay the glass, and then lay a piece of glass on top of that. You then dip your brush into the resin again and dab onto the glass until it is fully saturated and all the air bubbles are out, then repeat that process. Depending on the weight of the glass your using, 1-2 layers are sufficient to strengthen the helmet. After that cures up you can add a layer of the resin alone to hide the fiberglass texture if you desire. I personally like the look of the glass, but doing this will give it a smooth finish.
Also i have reinforced HIPS and ABS with glass without issues.
Also, fiberglass matt gives you a stronger stiffer result that the fiberglass cloth, which is woven like fabric. But either will work for this.