These are great questions, but I feel awkward hijacking a thread that isn't really about my experience. The Dateline NBC episode does a great job telling the whole story, including how I got involved. My Washington Post article explains how we persuaded the DA's office.
I am an autodidact, so diving into new subjects is something I naturally enjoy doing. The obsessive focus and intellectual flexibility that helped me in other areas, like computer programming and missile-defense research, worked just as well for forensics and criminal-profiling.
One example that sticks out is how I was able to refute the opinion of the FBI's top criminal profiler by going through and reading the reference text that is the equivalent of the DSM, but for behavioral analysis. He was listed as a co-author, so it would have been easy to assume that he was applying the standards correctly, but I was able to show that his thesis did not match the evidence.
The hardest question to answer is "why this case?" It is as close to a miracle as I've ever experienced ... some force I can't explain caused me to stay up late one night and watch an old TV-special about the murder on my computer, even though I don't watch TV and had zero prior interest in the true-crime genre.
The words of the accused professing his innocence before God were so powerful that, even as an atheist at the time, I felt compelled to look into the case more.
Being used as an instrument to correct a horrible injustice made me reconsider my belief in a higher power.