The process is the CCRC (who are non-governmental, but publicly-funded organisation) receives an application form the defendant, they then decide whether to review the defendant's case, if they do review the case and if they feel there has been a possible miscarriage of justice the CoA is then obliged to consider the case. The CCRC is not behoven to the defendant or their legal team to review the case, nor are the behoven to refer the case to the CoA, and nor are the CoA behoven to the CCRC to quash the conviction. Many applications do not lead to a review, many reviews do not lead to a referral to the CoA and often the CoA do not quash convictions.
It certainly it helps to have someone who knows what is likely to be considered important new evidence or important new legal argument, but however expensive the lawyers, they can't manufacture new evidence or a new legal argument from thin air (unless they're crooked of course, but I don't think that's accusation here).
Also once evidence of sexual history is allowed to be admitted the scope is clearly pre-defined and pre-approved by the Judge who will only approve the admission of evidence that is directly relevant to the facts or the prosecution argument (i.e. it cannot be used as just a mud-slinging exercise)
Now honestly I do not know if the verdict was wrong or right: I wasn't there, I wasn't at the trials and don't know the people concerned. All I know about the case is that which was reported in the media and the media are often selective about what they report.
I am not claiming to be an expert, and people are more than entitle to disagree, but I know a little about these processes and I don't think the criticisms are necessarily well-aimed. I feel there has to be a process for miscarriages of justice to be detected and put right and there has to be a process for all potentially-relevant evidence to be considered and I wouldn't like to see the legal system hamstrung in these regards.