Hose Clamp Salsa Watter Bottle Cage to Rigid Fork with No Sliding (Gravel)
Hose clamps should be more than adequate, although they will chew up the paint on your forks. You might consider an intermediate layer (could be as simple as electrical tape) to protect the paint. And of course give the setup a shakedown ride, and monitor it during the big ride.

There are strings that are stronger than fishing line (you can get carbon-fiber or dyneema yarns), but it wouldn't be feasible to tie them with sufficient clamping force.