The underlying concern of those who originally coined the phrase "nation of laws, not of men" was liberty and justice. Isn't your concern really to make sure that some men don't have arbitrary and capricious power over you or others?
The main way our nation became one of laws, not men was to prohibit ex post facto laws in the Constitution. That way, no government official or ruler can arrest someone and charge them with something no one knew was a crime when they did it. Of course, the other due process Constitutional protections such as Grand Juries, prohibition against self incrimination, etc., also are legal protections against arbitrary power.
Jury power to acquit on conscience is another protection from the sword of government. Jury power is another process of law review designed to protect liberty and justice.
The purpose of fully informed juries is also liberty and justice.
Both jury power and a nation of laws are designed to protect liberty and justice, so the two concepts cannot be at odds.
The "laws, not men" concept protects us before a law is written. Jury power protects us after bad law is written.
One thing that "laws, not men" definitely does not mean is that we should mechanistically or robotically apply law, no matter how unjust or inhumane the outcome. The very existence of the jury system was designed to put the common sense and humanity of the people in the process of administering law.
Our highest commonly held political value in this nation is not reverence for law at any cost. Our highest political values are liberty and justice for all. The law is a means toward the end of liberty and justice, and conscience is our guide toward that end.
We have coined a term for those who think the law is the end-all and be-all, higher than liberty or justice - LAW WORSHIPERS.
Law worshipers worship a false god - man's law (statute law). Our Founding Fathers talked in the Declaration of Independence about "the Laws of Nature and Nature's God". It is that higher law and the unalienable Rights to Life, Liberty, and the Pursuit of Happiness which our system should place at the top of our political values hierarchy.