The high school program I am in  has a half a year long project my senior year (like science fair, and we present it our school science fair, but more rigorous). I am working to getting my project proposal approved by my teacher.  My project is on time management when test taking. Overall, my teacher likes my proposal, but has one issue, which is the lack of any real incentive for the participants in my project to "try" on the test I would be giving them. My  teacher didn't consider a self-assessment question at the end of a project to be rigorous enough. Any advice that would help me to propose something to address this.

Since your teacher brought it up (good point, too), perhaps they (and perhaps other teachers?) might be willing to award extra credit for taking your test? It's hard to come up with a good carrot for high schoolers that's appealing to all, but applying some extra credit points to grades sounds pretty basic to students.

If you have enough participants, you might try splitting them randomly into 3 different groups to see if the incentive has any effect. One group loses 5 points for finishing late. Second group gains 5 points for finishing early. Third group is your control and gets no punishment or reward, just a normal test like any other day. Unsure this gets you where you want to be, but hopefully it helps generate fresh ideas. Good luck!