To clarify, I think there's an important practical difference between ranking multiple principles, vs naming one single principle of first precedence.
The former is what I think you've responded to, whereas the latter is what I was suggesting.
As you say, different principles often have tradeoffs, and can't be strictly ranked. But in any endeavor, we should observe that if we look hard enough, there is in fact always one ultimate principle of total importance.
For instance, in a game of chess, the be-all-end-all principle of first precedence is always to capture the opponent's king before they capture yours. But there are many sub-goals along that path that can't be strictly ranked. For instance, it's generally better to capture a knight than a pawn - but not always. Ultimately, the better move must be measured in terms of the overall goal of capturing the king. Nothing else matters except insofar as it contributes to that goal.
As you say - I think rather insightfully - people's intuitions about their own priorities are often different than their ability to consciously define them. But I think, when a collection of people come together to form a nation, then they must have some common goal in mind. And it is important for the people writing the constitution to be able to provide clarity on what that is. And I would suggest here that the one goal that we all share, which we all hope this nation will help us achieve, is to pursue our own happiness. Or perhaps even more vitally, to avoid misery.
Now that said, everything else will have tradeoffs - like is it better to live on the street, but have a reliable food source, or is it better to have a house, but unreliable food? Or is it better to have food, shelter, and water, but live in a jail cell - or to be totally free, but have all of your bodily needs in jeopardy?
It's hard to rank or weigh these things. But our guiding light is that, like moves on a chessboard, none of it matters at all, except insofar as it helps us avoid misery, and find happiness.
As you say, there will be times when the courts have to rule in cases where one person's avoidance of misery makes someone else miserable. And that's okay. At least we know that we are weighing the conflict on the correct principle.
To some extent, I think this speaks to your concern of flexibility, too. Happiness is a nebulous enough thing that it leaves room for interpretation. But we still pretty much know what makes us and others happy, what makes us miserable, and what we can learn to tolerate if it sets a precedent that we know helps us avoid misery in the long run.
Speaking of tolerance, I understand that I'm using it a little differently - I would argue more precisely - than it's generally used. But I think it's the most clear way to think of it.
Intolerance, I would say, is any time you take any action to make something stop. Whereas tolerance is any time you don't like something, but don't take any action to prevent it. All other definitions, to me, are fuzzy, and not worth using in a serious discussion. You might tolerate hearing you neighbor's video games, because you'd like them to show the same tolerance towards your piano practice. Whereas you might not tolerate them parking in your parking spot, and might show your intolerance by calling the landlord. Intolerance shows action, while tolerance shows measured inaction. That's the clear way to think about it.
As for the paradox of intolerance, the video linked below is an example of what I'm concerned about. This is by no means the only time I've seen or heard about something like this, but it's an example I could remember well enough to provide a link to. It's a video of Sam Harris describing a conversation he had where a woman said that you could not find any fault with the actions of a group of people of those actions were done for "religious" reasons.
https://www.youtube.com/watch?v=BW2y1z_ReVk&t=345s
This is a real problem we have in public discourse. And it does affect court rulings, too. For instance, in the Supreme Court's recent ruling on Groff v. DeJoy, Gerald Groff was able to be excused from working on Sundays, purely for "religious" reasons. In other words, because he happens to have a particular interpretation of a particular "religion", he gets special treatment that isn't granted to his co-workers. And this all stems from a societal fear of limiting people's ability to act out their religious opinions.
So I do think there's a problem, and I think it's appropriate to label it as a fear of expressing intolerance. Because the best definition of intolerance is any action, including speech, done with the goal of getting something to stop. And I think people in the western world are often afraid, certainly of limiting religious practice, but also of merely expressing criticism of people's religious ideas, as demonstrated by the video.