I feel like it would be best to leave this up to Conclave. In pre-trial, they already have the power to decide if evidence is “compelling” enough to bring it to trial, and they tend to dismiss charges if this bar is not cleared. Besides, if we want a legal standard for this, I think it would be better enshrined in the SOC than the Concordat.
Sure, nothing stops someone from immediately submitting a request for a new trial, but in the same way it would be denied on the basis of double jeopardy today, it would be denied for a lack of “new” and “compelling” evidence (with both words defined by Conclave for flexibility) after this amendment was passed.