Removability of non-Article III judges

Are judges of the U.S. Court of Federal Claims, U.S. Tax Court, U.S. Court of Appeals for Veterans Cases, the District of Columbia local courts, and -- drum roll -- the U.S. Court of Appeals for the Armed Forces removable with or without cause? Consider this exchange from yesterday's decision in Trump v. Slaughter:

Majority opinion, per Roberts, C.J. (at 28):

Nor do we determine the fate of officials not before us. In particular, as the Solicitor General recognized at argument, the permissibility of tenure protections for the judges of “non-Article III courts,” such as the Tax Court and the Court of Federal Claims, is not “presented” or “briefed” in this case and poses a “different set of questions.” Tr. of Oral Arg. 15, 28. We leave those questions for another day. All we do today is recognize what has been clear for a century— that those who fall within the President’s “general administrative control” must be removable by the President at will. Myers, 272 U.S., at 135.

Dissenting opinion of Justice Sotomayor (at 44):

The majority, for example, suggests that its rule might not apply to adjudicatory agencies, including non-Article III courts like the Tax Court. See ante, at 28. That is welcome news, but why is it so? As the majority explains, it cannot be because such agencies are exercising judicial power. Adjudications by Executive Branch agencies “are exercises of—indeed, under our constitutional structure they must be exercises of—the ‘executive Power.’” Arlington v. FCC, 569 U.S. 290, 305, n. 4 (2013); see ante, at 19. Nor, after today, is it obvious that such agencies could safely depend on a precedent like Wiener, which did address an adjudicatory agency but rested squarely on “[t]he philosophy of Humphrey’s.” 357 U.S., at 356. Still, the majority says, a narrow exception for non-Article III adjudicators might yet survive. If that is true, questions immediately arise: What, exactly, is the “‘different set of questions’” raised by these agencies?

Inside baseball question: if CAAF judges can be freely removed, what about CAAF Senior Judges?