First thing's first. There isn't any evidence that the 1867 quote is genuine. Historian Cynthia Nicoletti attempted to track down the quote for her book Secession On Trial, but the paper trail ended in a 1923 Lost Cause essay called "The War Was Not A Civil War". It was then reproduced in a couple of Jefferson Davis biographies in the mid-1900s before the quote made its way to the floor of U.S. Congress in the 1970s:

Two of Davis’s biographers, as well as numerous internet sites devoted to proving that Chase did not believe secession to be treason, have attributed the following quotation to Chase: “If you bring these leaders to trial, it will condemn the North, for by the Constitution secession is not rebellion.” Robert McElroy, Jefferson Davis: The Real and the Unreal, 2 vols. (New York: Harper & Brothers, 1937), 2: 540; Hudson Strode, Jefferson Davis, 3 vols. (New York: Harcourt Brace, 1955), 3: 250. These two authors provide no source for this quotation other than a reference to Johnson’s case report for U.S. v. Davis. The phrase does not appear in the case, and another somewhat similar quotation that McElroy attributed to Chase was actually uttered by Charles O’Conor. Case of Davis, Chase’s Reports, 12. The source of the quotation is mysterious, but it seems to have first appeared in Mildred Rutherford, “The War Was Not a Civil War,” Miss Rutherford’s Scrap Book 1 (1923): 12. Unfortunately, it has been reproduced many times, now with the new twist that Chase uttered it to Secretary Stanton. In fact, Senator Mark Hatfield referred to the quotation on the floor of the Senate in 1976, when that body discussed restoring Jefferson Davis’s citizenship. See Robert Penn Warren, Jefferson Davis Gets His Citizenship Back (Lexington: University Press of Kentucky, 1980), 94.

Moving on to the 1868 quote, this isn't particularly contradictory to the nationalist point of view before, during, or after the war. Despite my username, the only unconstitutional form of secession that was at issue was unilateral secession. Any state could (and still can) secede by mutual agreement, via the Constitutional Amendment process. If 2/3 of both Houses of Congress, and 3/4 of the state legislatures agreed, then they could make an amendment such as "South Carolina is no longer part of the USA", just so long as South Carolina agreed to it, per other terms in the U.S. Constitution.

See, for example, this line in Lincoln's First Inaugural Address, where he hints that the amendment process could be used for the purpose of secession:

This country, with its institutions, belongs to the people who inhabit it. Whenever they shall grow weary of the existing Government, they can exercise their constitutional right of amending it or their revolutionary right to dismember or overthrow it.

(Note that elsewhere in Lincoln's speech, he talks about the duty of the President and federal government to uphold the Constitution. Revolution was seen as an extra-constitutional right, while the Presidential Oath of Office requires the President to uphold the Constitution. Thus, the President had a duty to suppress a secession-fueled rebellion.)

So when Chase is writing that the states could still exist "disunited", this is probably what he is referring to, if he's referring to any specifics of a Constitutional remedy at all. Though again, all sides of the Civil War recognized the right of revolution, but Unionists believed this existed in opposition to the federal duty to uphold the Constitution. So revolution = war, as seen so clearly with the Civil War itself.

Discounting the 1867 quote and understanding the 1868 quote as only kinda/sorta tangentially referring to secession upon mutual agreement, I don't think it's fair to say that Chase actually did change his mind.

But what about the court in general? There is no evidence that any prominent federal judge really changed their mind on secession. I have written somewhat on this topic before. All eight Supreme Court justices alive at the time Lincoln took office in March 1861 all made statements -- either in the course of their judicial duties, or in private letters -- that they believed that secession was unconstitutional.

Most prominently is the quote by Supreme Court Justice Robert Cooper Grier, a Northern Democrat from Pennsylvania. Back then, Supreme Court justices "rode the circuit," which meant, when SCOTUS was out of session, they sat in session as one of the circuit court justices, in whichever circuit that they presided over. During this duty, Grier wrote the majority opinion in William Smith v. United States, also known as "The Jeff Davis Piracy Cases" (the ship at issue in the case was called "The Jeff Davis"). On October 15, 1861, Grier called secession a "miserable political heresy" and:

"The right to secede is not found in the Constitution, either in its letter or its spirit. If so, it would be felo de se [i.e., "a felon upon himself", or an illegal act of suicide]. It is a Government and Constitution ordained by the people of the whole United States for all time--not a mere temporary compact of independent and sovereign confederates."

Grier would go on to write the majority opinion in the 1863 Supreme Court "Prize Cases", an opinion not shy about calling Confederates "traitors" who were in open rebellion against the Constitutional rule of law. One of the more straightforward quotes is one in which he refutes the Confederate defense (as such) that the Confederates couldn't be "enemies" of the United States because they were U.S. citizens (and, yes, the Confederates did kind of want it both ways in this case, to hamstring the U.S.'s ability to respond by force of arms). Grier and the majority said, no, a U.S. citizen could be considered an enemy of the country, if they were committing treason, as was the case with the Confederates:

"They [Confederates] have cast off their allegiance and made war on their Government, and are nonetheless enemies because they are traitors."

But even in the dissent of the "Prize Cases", the court agreed that the Confederates were "in a state of insurrection," calling the war an "insurrection" more than a dozen times, and referring to Confederates as "insurgents".

Notably, the dissent in Texas v. White was written by Grier, who had already made his opinion known on secession. He did not dissent in the 1869 case because he'd had a change of heart, but because he believed that the secession question was irrelevant to that particular case. The other two justices who kinda/sorta joined the dissent were two Lincoln appointees, who had also signed on to the majority of "The Prize Cases", where "traitors" and "treason" are all over the opinion. Meanwhile, the majority in Texas v. White included the three living dissenters in the "Prize Cases". So, in other words, between the two cases, all the Supreme Court justices at the time had made it known that they believed secession to be unconstitutional.

And even the one Supreme Court justice who resigned to join the Confederacy actually didn't believe in the constitutionality of secession. Justice John A. Campbell understood that he was joining an extra-constitutional revolution. On November 26, 1860, he wrote a letter to his former law partner and current brother-in-law, which was published in his hometown paper the Mobile Daily Mercury on December 22, 1860. In the letter, Campbell characterized secession as a "coups d'etat" or illegal overthrow of government:

"...I have too much confidence in the constitution of my country to suppose that it does not afford a sufficient remedy in case of his [Lincoln's] wickedness. It is our pride and glory that for all the evils of government, there are constitutional modes of redress for every citizen. I am wholly unwilling to dishonor them before the civilized world, by any coups d'etat or insurrections against their authority except as a last resort."

He stayed on the court for three months after his home state of Alabama had seceded, only resigning after Fort Sumter made it clear that war had begun, and the Lincoln administration wasn't very interested in making concessions to Confederates.

Last but not least is this quote by Chief Justice Roger B. Taney, the most states right-y justice on the court and a thorn in the Lincoln administration's side until Taney's death in 1864 (he was very old). In anticipation of a secession case making its way to the Supreme Court, Taney began writing his legal opinion, found among his papers after his death:

"The South contends that a state has a constitutional right to secede from the Union formed with her sister states. In this I submit the South errs. No power or right is constitutional but what can be exercised in a form or mode provided in the constitution for its exercise. Secession is therefore not constitutional, but revolutionary; and is only morally competent, like war, upon failure of justice."

cont'd...

You might also ask in /r/SCOTUS. Someone there might have an interest in the case.