In their defense, they did exactly that. It wasn't until the police refused to look into evidence the police found at the house, refused to release the body of JonBenet for burial and would only focus on the parents that they "lawyered up".
Even after that the Ramseys continued to take lie detector tests (passed them all) giving hand writing analysis (neither of them) gave hair, blood and semen samples (no match).
In many ways the Ramseys were found guilty and sentenced by the press. Yet the police could not even get a grand jury, where ONLY the prosecution is represented, to come back against the parents.
Ahhh, the press. The great American Institution fighting for Truth, Justice and the American Way! [end sarcasm]
Umm, they didn't "continue" to take lie detector tests or "pass them all."
They refused and refused and refused to take any polygraph tests at all, even went to court to not have to take them. Years later, they paid a polygrapher to administer a private test to each of them, with only 3 questions on it.
Patsy had several inconclusives - John passed the simple test. They had a huge press conference to announce the private results and failed to mention the two days it took Patsy to pass the test and the several inconclusives she had first. They didn't even allow the first polygrapher (yes, it took two) to make a statement - his name had to be pulled out of them, at that.
It was all exceedingly dishonest. Lin Wood even lied about it to the public.
You also mentioned handwriting analysis. Patsy did not "pass" that scrutiny. They could not clear her.
They excluded many people, but not Patsy.
As far as not releasing JBR's body - the Ramseys had already just gone off and left her lying on the floor of their living room and were preparing their plane to leave town immediately. They didn't seem too concerned about getting her body or staying with it.
And you do not know what the Grand Jury concluded. NO ONE does.