An example from what I’m dealing with now: according to Jewish law as stated in the Talmud, a synagogue should be at the height of the city, and simply understood—and this is how the halakhic decisors understood it—the intention is the city’s highest elevation. (And in practice that’s not how it is.) But Lieberman and several others understood it differently (and they have several nice proofs): that the intention is the city center, or the most important place in the city.
Would you rule that way?
It’s not a dramatic question, but as an example.

Definitely. Why not? After all, this is an interpretation of the law in the Talmud, and if I am convinced that this is the plain meaning of the Talmud, why shouldn’t I rule that way? That is the true adherence to the Talmud. That indeed is the meaning of first-order halakhic ruling, but it has no connection to whether the wording or the reasoning is forced.
By the way, with this law too, even according to its accepted interpretation, they are hardly careful about it anywhere.

Why do you follow the words of the Talmud and not an earlier layer, the acceptance of the Jewish people, and so on?
Isn’t this in the Shulchan Arukh?

Because there is no earlier layer. Do you mean to rule Jewish law based on the Book of Job or Jeremiah?
The Shulchan Arukh was not accepted in that sense. Even its commentators disagree with it. Of course it carries weight, but it does not have mandatory authority.

Maybe second-order halakhic ruling itself is something that was accepted?

As the Kotzker already said: against the truth, there is no majority.
And besides, you can’t turn everything people happen to do into a binding acceptance. Otherwise you completely fossilize the whole world. I do what the medieval authorities (Rishonim) did: they ruled according to their understanding of the Talmud even without precedents (and of course that also creates precedents for those who, for some reason, will want to issue second-order halakhic rulings in future generations).