This is not a direct answer to your shipwreck question, but it is worth pointing out that your question appears to presume that the coronation would have happened only when the previous monarch was finally declared dead, and that the coronation itself would be the start of Elsa's reign.

This is a popular misconception of the history of coronations. A monarch's reign does not "start" when the crown is placed on their head in an elaborate ceremony. Rather, coronations were retroactive celebrations and public acknowledgements of the new monarch's reign. Until about the 1200s, this tended to be either on the same day, or only several days, after their reign de facto began, but it gradually slipped later and later for various reasons.

If we're using UK coronations as an example, King Edgar's happened 15 years after he became king. For Edward it was 2 years. For William I it was 3 weeks. Henry VI was actually crowned 7 years after his father died, but did not actually reign as king for another 8 years. The timing and stated purpose of the coronation was quite inconsistent.

As of the 1700s or so, it was considered inappropriate to have a coronation, which was supposed to be a celebratory event, within a certain amount of time (months to years) after the previous monarch died, as everyone was supposed to be officially mourning. And since George VI, every monarch has waited at least a year.

In other words, fantasy Disney story and suspension of disbelief aside, there is not necessarily any relationship between the 3 year timing of Elsa's coronation, and when the people collectively decided her parents were probably dead.

A period appropriate comparison would be the Franklin Expedition. (Fandom sleuths have also determined that it was in fact Elsa who caused the unusually cold conditions of the 1840s, which lead to the pack ice not breaking up in the summer of 1847, and that therefore Elsa killed the Franklin Expedition. But that is neither here nor there). Your hypothetical involves a ruling monarch disappearing on what was supposed to be a short trip instead of a years long expedition into the unknown, however, so comparison is limited; perhaps someone else can chime in with other examples of unexpected disappearances at sea.

The Franklin Expedition departed England in 1845 to search the waters of Northern Canada for the last link in the Northwest Passage. It was expected to spend at least one winter in the ice, and was provisioned for up to three years in the north. So there was no concern when no word was heard from the explorers in 1846; a second winter in the ice was expected to be well within the expedition's' capacity to survive. By the time the 1847 summer season was ending and no word was yet heard, though, concerns began to be raised. Lady Franklin, wife of the expedition's commander Sir John Franklin, was famously proactive in organizing rescue missions and relief efforts from both the admiralty and private enterprises. The first such rescue missions were sent in the spring of 1848, while many of the missing men were likely still alive. However, even reaching and sailing in the arctic is an incredibly difficult and complex endeavor, and multiple rescue missions had difficulty keeping their own crews alive, let alone find surviving men from the lost expedition. The rescue efforts to find the lost expedition were enormous, and it was actually in large part due to the search for Franklin that the last links of the Northwest Passage were at last charted. By the time the first major clues about the expedition's fate were found in 1850, there was still some tenuous hope that there might yet be survivors; however it was far more likely that all members were dead by then.

Lady Franklin persisted in believing that her husband and some of his men might still be alive far longer than most others did. The Admiralty declared the expedition members dead in 1854 and ceased further rescue missions. Lady Franklin continued to fund private expeditions up to 1857 and beyond, even though the cairn note found in 1859 confirmed that Sir John Franklin had died in 1847.

For a thorough overview of the rescue efforts made to find the Franklin Expedition, see Watson, Paul (2018), Ice Ghosts: The Epic Hunt for the Lost Franklin Expedition, W. Norton & Company.