I would think fiberglass would work if done correctly as long as its not a Poly proplene or simular plastic. If that is original then I would think it is not plastic. Plastic was not widely used back then. That was still the time of Bakalite. Bakalite would not have been used for something that size.
Our 59 the shower pan is fiberglass but it looks like plastic from the top.. I would think yours is fiberglass as well but it may just be gel coated on both sides and look like its plastic.
Reguardles as long as what ever it is is not a material that is prone to continual skinning like a Poly propelene is it should work fine. Just be sure to sand the area where you want the material to bond. Fiberglass does skin when it cures out and you have to sand past that layer and then it will bond quite well.
www.westmarine.com is where I have been getting my glass stuff. That have a good network of stores and may be one close by. Little pricy but conveinent for small quanites.