They problem with speeding up the appeals process is the guys who really are innocent get shafted...
Up here in Chicago, they suspended the death penalty two years ago because they found too many people on death row were walking out because new evidence proved their innocence. As a matter of fact, the police dept I work for (and several of the people who I work with, and consider good friends) were involved in a similar case several years ago...
Could you send somebody to death knowing that there is the slimmest possibility that he is innocent?