Ive never seen a battery terminal melt, has to be scary, Im fairly decent with fiberglassing things, I was wondering why didnt you put any resin on the white spots on your doors mainly around the speaker rings and where your fabric meets the door?
Also I think you mentioned wrapped the doors with some sort of material. You need to get that fiberglass as smooth as you can because the bumps will show thru the material.
Sand the glass down as much as you can and then apply a thin coat of body filler on top of it and sand that smooth, this will fill in most dips and equalize the surface.
There is a trick i use for this. Take some body filler and thin it out with resin, I usually thin mine out enough so that I can paint it on with a paint brush. Use the require amounts of hardener for filler and resin. Although this method will be a lil harder to sand but nothing thats not manageable.