However, I think a variation of the idea would be constitutional: within the Supreme Court, Congress creates two divisions for purposes of appellate jurisdiction cases (they would stay unified for original jurisdiction cases to avoid a constitutional problem). Justices would be assigned to only one or the other, no overlap. One division handles constitutional appeals, one division handles other cases.
Congress could also remove the appellate jurisdiction of the court to hear claims that laws are unconstitutional, leaving the only appellate jurisdiction as claims that officials are acting illegally or unconstitutionally or disputes of lower-level decisions as incorrect.
I'm not saying this is necessary good policy, but it would be constitutional.
Yes, it does. Jurisdiction literally means the ability to say what the law is. There is no plausible definition of appellate jurisdiction in the Anglo-American legal tradition that would not involve the power and duty to reconcile incompatible sources of law.
> Congress could also remove the appellate jurisdiction of the court to hear claims that laws are unconstitutional
No, it cannot. First, the power to make "exceptions" does not imply the ability to completely remove power. Second, whatever power Congress had under Article III was limited by later amendments, e.g., it cannot remove jurisdiction in a way that results in an impingement on the right to due process under the Fifth Amendment. There is nothing in the text of the Constitution nor in any case law that would support your implicit contention that Article III is somehow immune to being subject to the amendments process.
Third, although Klein has been a bit disfavored lately, it was reaffirmed in Patchak only a couple years ago. Some commentators focus on the plurality opinion while ignoring the fact that they're only a plurality and not the dissent because of Ginsburg's and Sotomayor's concurrence. That opinion interpreted Congress's intent generously and reasoned that Congress merely amended its waiver of sovereign immunity rather than dictated a result in a particular case. Of note, the concurring opinion explicitly agreed in principle with the "dissent," and they still ruled substantively on the merits notwithstanding Congress's attempt to strip jurisdiction.
If you'd like to continue this, please read Chemerinsky's excellent hornbook on federal jurisdiction first. And, you know, maybe go to law school.
I'm not disagreeing with the other examples you gave, including about original jurisdiction - clearly separation of powers and the constitutional structure are both real and binding. But equally, those concerns don't prevent the kind of personnel regulation we're discussing.
Congress can ordain and establish inferior courts, and can regulate the appellate jurisdiction of the Supreme Court. However, it cannot regulate much of the judiciary outside that. For one, it cannot expand the Supreme Court's original jurisdiction. Marbury. Nor can it dictate how the court applies the law. Klein. Congress's power over the federal judiciary is constrained and there is no basis in the text of the Constitution or in any case law to support your position.