Not to put too fine a point on it, but I think the OP is engaging in the fool's errand that is attempting to evaluate SCOTUS's jurisprudence through the lens of conventional partisan politics. Which often ends badly as, outside of hacks men like William O. Douglas -- who wore on his sleeve that he thought of himself as a black-robed super-legislator -- most judicial decision-making has precious little attachment to the considerations of conventional partisan politics. While it is undeniable that there is a correlation between personal political beliefs and judicial philosophy, correlation does not equal causation. A fact which even I still need to remind myself sometimes when I read Sotomeyer's opinions. (Full disclaimer: I am a dues-paying member of the Federalist Society and was, too many years ago, president of my law school's student chapter.)
But to try to make a good-faith effort to respond to the thread's premise, if you want a less successful and ascendant originalism, you need to not provide it such fertile ground to take root in. As the originalism developed by men like Robert Bork and Antonin Scalia was the intellectual backlash to the near-total triumph of legal realism as a school of judicial philosophy. It is difficult to convey, by the mid-Sixties, just how thorough legal realism's command of the bench was, as not only had it bested rival schools of judicial thought and displaced them as the primary method of judicial decision-making, but had so thoroughly discredited the alternatives that it had become the only school of judicial thought. I will refrain from addressing whether that was a good thing for fear of kicking up discussion of contemporary politics, but legal realism's primacy bred a considerable amount of intellectual laziness amongst its practitioners, with it becoming a bit of a habit of SCOTUS's majorities to determine the correct answer and then reverse-engineer the reasoning for their decision from there. The most infamous example of such is, surprisingly, neither Griswald nor Roe (though the latter certainly does deserve an honorable mention), but rather Furman v. Georgia, in which every justice wrote a concurrence or dissent and the majority concurrences could not agree upon a common rationale for their holding beyond that the holding was, in fact, the correct one. Against the backdrop of the hangover from the Warren and Burger Courts' excesses, it is scarcely surprising that a craving for a more structured and grounded theory of judicial decision-making would manifest itself. And so long as such is desired, when the political consequences of the Warren and Burger Courts' decisions make themselves felt and there becomes a political market for an alternative to legal realism, you're going to have a long march through institutions similar to originalism's for whatever develops to satisfy the intellectual need which OTL's originalism did.
So if you want less originalism, you need to nerf legal realism's successes in turn. How precisely you choose to do that is itself an episode in going down rabbit-holes, as "nerf legal realism's successes" can range from everything to the simple expedient of butterflying William Brennan's appointment to more elaborate and fanciful projects like an entire alternative 14th Amendment P&I Clause jurisprudence which butterflies Plessey and makes much of the Twentieth Century's legal history utterly unrecognizable from its first- and second-order effects. As opposed to "simply" having Eisenhower avoid recess-appointing Brennan, whose first-order effects are just the ones that unleash all of the butterflies, with -- just for a start -- the entirety of modern abortion jurisprudence going overboard as Griswald, Roe, and Eisenstadt all are unrecognizable without Brennan's backroom political skills in putting together majorities.
