Whether an Article III habeas court must grant relief when convinced a state court's judgment violates the Constitution despite AEDPA deference

If, after carefully weighing all the reasons for accepting a state court’s judgment, an Article III habeas court is convinced that a prisoner’s custody and death sentence violate the Constitution, and if, after an independently -rendered interpret ation of the state court adjudication , the Article III court finds it an erroneous structural Constitutional violation with no factual foundation to support the erroneous state court interpretation, must that Article III court interpret section 2254(d) (1) in a manner that avoids an unconstitutional infringement of the Article III court’s mandated powers and duties and grant relief? Alternatively, if, in adjudicating a capital case, an Article III court denies any remedy for a Constitutional claim it ha s independently adjudicated to be meritorious and with no factual basis in support such that the Article III court defers to that “clearly erroneous” interpretation of the Constitution in applying section 2254(d)(1) , does that “deference ” violate Article III and the Supremacy Clause , thereby effectively suspending the Writ ?