They have the talent,
I hope you are right. I do not know enough about them to judge. The paper did not tell me anything about their work.
No one has provided an answer to it yet.
Well, some of us did give answers, but there is no consensus of opinion. There cannot be, because no one can know the answer.
But let me repeat my best answer, which sounds facetious, but is not:
Q: "What is the highest priority experiment the LENR community wants to see conducted?"
The answer is in the process, not in any specifics about the actual experiment. It is not possible to know what experiment is best, so instead of trying to determine this, you should structure the project with the best likelihood of finding the answer. I recommend Harry Truman's method:
Find some young people who are very good at experimental science and very anxious to do cold fusion.
Ask them what they want to do, and tell them they should do that.
Stay out of their way. Give them whatever equipment they need. Do not attempt to direct them, second guess them, or even understand them. Most scientific progress is made by young people who do not know where the limits are or what is supposedly impossible.
That's it. That's all there is to it. That is how every fundamental breakthrough in history was made, as far as I know. I have never heard of one that was planned ahead of time, or one in which people had any clue what to do before they did it. Of course if you are designing a new computer or an airplane, you have tons of textbook information to go by. That's entirely different. Someday there will be thousands of pages of textbooks telling people how to do cold fusion, but at present there are only a dozen pages or so. The "how to" papers by Storms and Cravens, and the recipe by Mizuno and me. That's about it. Several thousand pages more will be needed before cold fusion can be made practical. That is something Seven_of_twenty and others fail to realize.
The experimental literature has many hints, but for the most part you need to read between the lines and synthesize your own understanding. There is nothing explicit because the authors themselves do not know.