The only thing I could suggest, as have before, is still putting resin on the outside, but in very very thing layers. It will take some time to build up enough layers to stiffen the paper. If you make the layers to thick it will weigh the paper down, make it sag and you will be forced to start over.
You could try sealing the paper first so that it does not absorb the resin. Try sealing it with elmers glue by "painting" a layer on, but again you will have to layer it with very thin layers to not cause the paper to sag.
1.) Squeeze glue out of the bottle onto a paper plate or equivalent, using a sponge, "paint the glue onto the surface starting with the base of the helm. Work your way up allowing it to dry as you go.
2.)Once sealed with glue, use the same procedure with resin on the outside. Start at the bottom working your way to the top in rings around the helm, allowing to dry between each successive ring. By ring I mean start a the bottom and cover up 2 inches, allow to dry. Work you way up another two inches, etc. till completely covered.
3.)Fiberglass or equivalent the inside once it has become sufficiently stiff. By stiff I mean under slight pressure it does not deform, but don't try sitting on it lol... resin is tough, but I am not sure how large you are....
Keep in mind, the slower you do this, the less your helm will sag, slow enough, and it wont sag. It will take patience. This may take more than one, more than two days in fact, to complete.
One other hint, if you mix in a little extra hardner into the resin, it will harden much faster, but as you will be working with smaller areas this wont be to terrible. Apply to small areas quickly. One draw back is the extra hardner will make the resin more brittle when cured, but if you fibergalss the inside this wont be an issue.