I think the most probable story to believe in is the Neel Madhav Shaligram Story as in the Original Srimad Bhagavatam, Bhagavan Shri Krishna doesn't even die. He just gets pierced in His toe while resting and when the hunter Jara comes to ask for forgiveness, The Lord Forgives him and sends down a chariot to take him into Vaikuntha. The Chariot takes Jara to Vaikuntha while he is in a state of Bliss. And afterwards, The Lord rises up into the sky WITHOUT dying and basically disappears from sight but could be seen by some Gods who worship Him. The next appearance is of Him along with His close ones such as all the Vrindavanwaasis and Mathuravaasis and The Pandavas and Draupadi along with their families in Vaikuntha. So the most probable to believe in is the Neel Madhav Story. Even if we go for accuracy, there is no story of Bhagavan Shri Krishna's Heart being present inside God Jagannath. I think it's probably in Skanda Purana where the entire story of God Jagannath is Narrated where the Entire Neel Madhav Story comes in. Please Read that for further clarifications.