That info you provided helps a lot. My recommendation is this. Skip the PVA and wood glue. With the method you are using, it is not needed and also will cause more damage than help... as you have noticed.
Using your self adhesive fiberglass, carefully cut out pieces and attach them to the outside of your cardboard helmet. Do this to the point where every part of your helmet is covered and make sure there are zero overlaps or gaps. It will also help immensely if you use it to overlap the seams where cardboard pieces are connected. I won't lie, this will take some time and patience.
Once this is done, apply a VERY thin coat of body filler over the fiberglass. Just enough to fill in the squares of the fiberglass and maybe just a hair over. This will be your baseline - a point and indicator of your limit to sanding. Do not sand past this point or you will run into trouble. The fiberglass in conjunction with the body filler will act as your hardener. Since you are not using cardstock, you really don't need too much more strengthening. The corrugated cardboard with hot glue should be pretty strong, and using the fiberglass with body filler should be stronger than PVA. Be careful not to stress it too much as it can crack (PVA would do the same), but the fiberglass should help reduce that possibility, and will limit the size of the crack should it happen. Once you have done all of that, you can proceed as normal. Add thin layers of body filler and sand to fine tune the shape.
For these questions regarding Aqua Resin, I highly recommend you contact Glasscutter and maybe he can offer some assistance. Added benefit is he too is in Washington State
EDIT: Go figure, he beat me to it! I swear, he has a notification sent to his cell phone whenever "Aqua Resin" is mentioned here!!!!