I am aware of the criteria of the THINK award but I haven’t found much info on how teams set themselves apart when trying to win this award. I really want to go for this award next year.
If you have won this award, What did you do to set yourself apart?
This article should be useful for one aspect. It shows that some things you say in interviews can help.
I am glad that you are attempting to get more awards.
My team won the Think award at the Pikes Peak signature event back in February, and to be completely honest, I’m still not entirely sure why. 
Going off of the criteria, however, there is a large emphasis placed on autons. We have odometry on our robot, which meant we had a very reliable match auton and skills, which is one of the judging criteria. Further, I wrote a computer program (which, we showed the judges in our interview), which allows a user to draw a path on a map of the field for the robot to follow using Pure Pursuit and the odometry, which, now that I think about it, probably contributed to the award as well.
Ultimately, I’d recommend working on a strong, consistent auton (in matches and skills), and I also STRONGLY recommend maintaining a great notebook documenting the code (something I, admittedly, struggle with). Finally, using your code to think outside the box and come up with an innovative solution to something is your best bet to set yourself apart from other teams.
Hope this helped!
Our team has won several think awards, the highest of which was at the state level in Indiana, one of the more competitive states. Our team always focused on creative programming, and I found us an interesting experiment because we never had anything more than a middle-to-upper-middle of the pack Auton skills, but our creative programming, like using the GPS or using moving averages to detect game objects, was enough to convince the judges. Additionally, my whole team was very well-spoken and truly loved programming, so by speaking naturally, creatively, and passionately without needing to script anything or have the judges ask questions to spark conversation, my team was able to showcase our programming skills. Good luck!