Use the potion on a villager that makes you feel "light and springy". Put the villager under the cliff with the gem. The villager will spring up, snatch the gem, and bring it to the door.
After your fire has burnt for more than ten hours, you will see something sparkling in it. Allow the fire to burn out to find a gem in the ashy remains. It will be too hot to touch at first. Bring a villager to the waterfall. You should have an action with something to do with putting water on it. Repeat this until the villager does not put any more water on it. Drag a villager to the gem and they will put it in the door.
Rebuild the statue and there will be a gem. Give it to a Master Builder to "finish" it. Give the finished gem to the chief. The chief will bring it to the clam, then get the gem inside the clam. They will bring that to the door.