Is there is DNA evidence available which could either exonerate the convict or confirm his guilt, it should be used.
By the same token, if the DNA evidence confirms his guilt (as it will in most cases), then far more expensive and duplicate appeals should be terminated and a quick date with the hangman should be set.
Potential embarrassment of judges, prosecutors or others involved with a phony conviction should play no role in the process.
There are multiple avenues of appeal. The fact that one does not pan out should not preclude other avenues of appeal.