Even 15 fundamental ideas would be good. Ever since I read Personalities and Methods, I’ve been wondering what could be done in that style regarding the medieval authorities (Rishonim), and then to keep going further. (Even in Personalities and Methods, at least for me, it seems that mainly with Rabbi Chaim and the Rogatchover one can really grasp something systematic.) An attempt to distill characteristic questions, foundational ideas, and some kind of technique. I’m not familiar enough with the literature on the subject. Ta-Shma did something on Rabbi Zerahiah HaLevi (not what I’m looking for), and Rami Reiner did something on Rabbenu Tam (even farther from it). I vaguely remember seeing something on Nachmanides too. But you’d need a great talmudic scholar with well-developed philosophical and methodological reflection. Regarding the Tannaim, it seems there is even less, also because there just isn’t enough material. And maybe there really is no method in creative Torah interpretation.

Though between Beit Shammai and Beit Hillel, since a common denominator already exists and is quite conspicuous—stringency versus leniency, as already in the Mishnah: “these are among the leniencies of Beit Shammai,” etc.—it sounds reasonable that if one is looking for an essential connection, one should look for it in something abstract and general that naturally gets specified across all the disputes. And see: https://did.li/mikyab-BetHillelBetShamai.

Beit Shammai had a stronger superego.

Tirgitz, Aryeh Hayon wrote a doctoral dissertation on Beit Shammai and Beit Hillel, but what I wanted to know was whether there is really something to say here—that behind a hundred disputes there stands one consistent underlying principle.
By the way, why are Ta-Shma and Reiner far from what you’re looking for? What exactly are you looking for?

I don’t really know what I’m looking for (and presumably many others are looking for it too). To try to “crack” the figure: what are the lines of thought unique to him, so that, for example, one could use those same “tools” elsewhere. And maybe it would be possible to create maps like that and place figures on them, with connections between them, and trace the history of the talmudic/intellectual spirit.

Maybe also to make some basic estimate of what things would look like if there is no method in creative Torah interpretation. If there are ten topics, and in each topic three options are open, and before us are two medieval authorities (Rishonim), each of whom randomly picks one of the options in each topic with no systematicity whatsoever, then on average there would be disagreement between them in two-thirds of the topics, without that indicating anything at all. So in order to be convinced that it makes sense to look for a common denominator, you’d need stronger statistical significance.

It seems that in the law of a rival wife, Beit Hillel were דווקא the stringent ones and Beit Shammai the lenient ones.

Beit Shammai prefer to read the verse according to its plain form even when that goes against reason, whereas Beit Hillel prefer interpretive exposition. Beit Shammai also prefer not to make distinctions in prohibitions, even where distinctions should be made and some cases permitted; instead they prohibit everything. That, of course, leads to many stringencies.