My sense, personally, is that mostly that people have the causality on legal formalism reversed: originalism is not a theory that leads to conclusions, it's a rationalization used to support conclusions already held.
But at the very least what you're saying is something worth thinking about. Given that Oyez makes every supreme court oral argument public and the filings are clearly public, it seems like there probably would be a case for any number of text learning methods to try to identify formalist style in legal arguments for an analysis like this.
I never understood this logic, because it's inconsistent with how judges & justices like Scalia often found in favor of litigants he despised, because they had a strong originalist argument. Breyer on the other hand, with his 57-factor balancing tests, always finds a way to find in favor of his favored side.
That doesn't describe Scalia at all. Scalia applied originalism when it suited him, and abandoned it when it interfered with his ideological goals.
Scalia like most SCOTUS justices, cared little for the actual litigants, since they were largely irrelevant to the matters at hand other than as vessels for bringing the matter to court. Due to the length of time it takes cases to get to the Supreme Court, many of the named litigants aren't even the original parties, the original parties having long since died or left office.
The facts of the litigants don't matter to the legal reasoning, because SCOTUS decides matters of law, not fact.
Those situations aside, I think Sotomayor and Ginsburg's emotional appeals in oral argument are representative of how they are actually deciding those cases (i.e. for reasons related to the specifics of litigants), and that the written opinions may simply be a legal veneer over their true motives.
It's called "original jurisdiction" and for SCOTUS their scope of original jurisdiction is limited to cases between the states or involving ambassadors or other "public ministers." As a portion of SCOTUS' load, such cases are such a small fraction that it can be decades between such cases.
SCOTUS otherwise does not decide matters of fact because it's not within their jurisdiction to do so as an appellate court. They can overturn lower-court rulings on the facts, but in doing so must remand to the lower courts for new rulings on the facts. Additionally, while they can take facts into account in their rulings, such facts must be part of the record established in the lower courts (i.e., the trial courts), unless it is a case of original jurisdiction for SCOTUS (meaning state vs state cases).
In natural sciences, a theory is a set of hypotheses, along with their logical consequences with the aid of auxiliary theories. This is not what judges to. They have a set of meta-principles(originalism, textualism, precedent, etc) and heuristics (for reasonableness, fairness, etc). They use them to come at a decision they favor. The difference between a Breyer and a Scalia is the way they assign weights to these heuristics and meta-principles to favor their decisions.
Conversely, it could be said Scalia twisted the idea of "originalist" to suit his political ends. Heller in particular is a very consequential ruling that basically invented a new right under the second amendment from whole cloth. When originalists complain about "activist judges" it can seem intellectually dishonest.
There's also a good question about how originalists can even support Marbury v Madison and the concept of judicial supremacy in the first place, since it doesn't originate in any law. Right now they support it because they have durable power in the courts.
As to Marbury v. Madison, even (some) originalists believe in stare decisis, though it is a controversial topic.
In other words, originalism considers unintended consequences to be outside the scope of the law, whereas textualism considers them to be within scope.