Completely stuck with nonsensical project
I think you should stick with it.

As far as my understanding goes, publishing 1-2 papers as a mathematics PhD student is (more than) enough to get your degree. It may not rank you as a star but it's a solid proof of competence. Working on other lower risk projects may not improve your thesis significantly. Successfully completing a high risk project, however, will be a boon to your PhD.

Furthermore, this project yanks you out of your comfort zone where you can gradually work towards a solution. Instead, you now have to find one key idea and you're basically done. Again, you've already shown you're a good mathematician inside your comfort zone, so showing that you can solve those kind of problems should not be your main priority.

I think your advisor has a high opinion of you and wants to give you an opportunity to prove exactly how much you're capable of. That's a nice vote of confidence. If you actually do want to stick with it, it's probably a good idea to find ways to enjoy the project. Possible ideas: talk to other people about the project, especially to your advisor and the other two professors. Sometimes spend as much time as possible trying to find a solution even if you feel it may not work. And sometimes work on unrelated fields or do other stuff (such as teaching) that is both inspiring and relaxing.