This ship is likely to be the Dawn Runner
The Dawn Runner is the ship of Balandar Brightstar. It ran aground somewhere in Dustwallow Marsh. Ithania is the first mate of the vessel. The rest of the crew is unknown (and dead).
Note
According to Brightstar his loaded ship ran aground somewhere in Dustwallow Marsh, and was subsequently looted by Theramore marines. There is a ship that fits all the criteria for this description, being 1) an elven ship, 2) wrecked on the shore rather than sunk below water, 3) having lots of cargo scattered about, and 4) being close enough to Theramore for the population there to notice the ship.