That won't be sufficient for a few reasons. First, in a significant number of cases where people have been exonerated for crimes, they were convicted based on the police coercing testimony, hiding evidence of innocence, and even fabricating evidence. Based soley on the evidence presented, the jury should have convicted, even with a higher standard.

Secondly, the more serious a crime is, the less likely that jurors are willing to let the accused off on a "technicality". Even if they are told they need to judge to a higher standard, their inclination is to judge to a lesser one and this will subconsciously influence their weighing of the evidence.