Hi abullard,
Your observation, "in the thick of the exam when your heart is beating in your ears and you're in full panic mode," perfectly captures one of the reasons that the LSAT can be so difficult to take, especially when you are taking it for real.
It can feel like a very high stakes, high stress situation, somewhat similar to performing a musical instrument or an athletic competition in front of an audience, or to public speaking.
The key to optimal performance, for the LSAT (and likely for those other activities), is sufficient practice before you get to taking the LSAT. Long before you take the LSAT, you should be studying/practicing each of these concepts, question types, etc. untimed at first. Start by learning the correct way to approach each question. Speed is the last thing that comes, so first worry about accuracy and understanding.
When you do get to timed sections, it's important not to deviate from the correct way that you have been practicing. Unfortunately, some students panic when they take their first practice test after having done a lot of studying, and they throw out everything that they've learned/practiced because they are so worried about the time pressure. It's better to do the questions correctly even if you don't finish the section than to try to rush and not follow your game plan.
In this question, for example, before you even look at the answers, ideally you should have a solid prephrase of what is wrong with their plan. If the goal is to offer the scholarships to the most highly evaluated auditions, then why aren't they just offering the scholarships to the top 10% of the auditions? Splitting the scholarships between local and non-local doesn't make any sense. The locals could be terrible, for example, and they are winning scholarships over Broadway actors!
While D may be worded differently than our prephrase, it's important to slow down when reading each answer and not rule out an answer that is confusing. If you're not sure about an answer, leave it as a contender. Then, once you're just left with any remaining contenders, then really compare them and see which is best. There are times where you may correctly select the right answer without even being 100% sure what it means as long as you did feel confident that the other answers were not what you want.
As for test anxiety itself, here is a link to a list of great resources on test mentality.
https://blog.powerscore.com/lsat/the-ul ... urce-list/