Any reason you rule out epoxy? It is the gold standard. Full size planes are made with fiberglass epoxy. The second choice is polyester resin. You won't see it on real airplanes but most all fiberglass boats use it or vinyl ester resin which is slightly better than polyester.
@Tench745 is right it depends on the application. If you are sure that it will always be in tension, just about anything will do. Say... if you are sure you'll never pull negative G's, the bottom skin could be stuck with anything. In compression, however, the resin is critical. The resin is what keeps the individual filaments (~ 10µm) from buckling. Thus the strength of the laminate is largely dependent on wetting every filament. When laying up fiberglass with epoxy or polyester, if it looks hazy, it's not wetted. If totally clear where you could read through it, it is wetted properly. Every filament is being supported laterally so they don't buckle and thus contribute to the ultimate compressive strength of the laminate (layer) you're applying.
I agree here also. If you don't want to start over, you might find scuffing it up with sandpaper might help (might not). But only if you are willing to use epoxy. Epoxy works mainly by mechanically gripping on to things, not chemically fusing. If you give it something to grip (sanding) it might stay on better. Polyester or vinyl ester resins are NOT good for mechanically connecting. But as @quorneg, said having the glue of choice seep into the paper surface would give the ultimate strength.