My family plays CE a lot and so the tip of the gate/cone is getting frayed and "soft."

Does anyone have solutions to strengthen the tip without ruining the aesthetics?

I tried laminating an older ffg cone and it looked horrible.

You probably don't need this info anymore but putting super glue in the middle layer is the best way I know to fix/strengthen cardboard composite. I've actually used a razor blade to split things I know will become weak and apply super glue to them, including my hyperspace great. Just don't go nuts with the glue. you want it to soak into the cardboard layers but not to soak the outer, glossy layer (the art layer). Too much glue can cause bubbling. I normally only split at sharp corners and use a drop of liquid glue per 1-2 square cm. An applicator with a needle works best to avoid creasing the cardboard.