Kent Scheidegger, legal director of the Criminal Justice Legal Foundation stated, “It is a very strange argument to say that a murderer can delay justice with protracted appeals for decades and then turn around and claim his own delay as a reason to escape his deserved punishment altogether".
Although that was tried in the case of Manuel Valle in 2011 it failed. He was convicted of killing a police officer in 1978 yet his execution didn't take place until 2011, 33 years later. His attorney appealed to the Supreme Court for a stay just hours before his execution. While the stay was refused, it sadly had one dissent from Stephen Breyer who claimed that being on death row for that long amounted to cruel and unusual punishment. What makes that dissent bullshit is that it was the criminal and his attorney that filed appeal after appeal after appeal . . . after appeal causing the lengthy death row time. If anyone treated Valle in a cruel and unusual manner it was himself and/or his attorney.
As far as what you suggest about another court hearing nothing but death penalty appeals, it could easily be done by an act of Congress based on Article III, Section 1 of the Constitution.