In one of the Hornblower novels, a ship-of-the-line he was aboard became similarly stuck and the tide was running out. He had every gun turned as far forward as possible and put all hands possible on the capstan. He then fired both broadsides simultaneously while the hands at the capstan heaved for their lives. A second time freed the ship.
I have no doubt-can you imagine, being in some locale in a ship-of-the-line, stuck hard with the tide going out, especially if you were in either a hostile area, or an area where you might be seen by higher command!
I don’t doubt for a second that every single gambit was employed-you could imagine having the entire crew running from side to side trying to rock the vessel, guns firing, heaving at the capstan in unison!