I've added the east lothian version of the story I learned to the folklore section beside the Well O Wearie.
I have cuthill as from Cuithail meaning "fold" in the first place name resource I looked up. Being a lowland name may mean it's saxon or brythonic in origin though. I'll look into it. Often a brythonic name would be replaced with a scots or gaelic one which sounded the same, but actually had a completely different meaning, as in the case of Loch Lochy, which gaelophiles give as meaning the loch of splendour, but which folklore gives us our clue to its brythonic meaning, as it has always been known locally as maiden loch.
There's a black well at Culloden, it's other name is the well of the dead, so perhaps the name of the well relating to Cuthilldorie has changed to something more english or more christian over time, and looking at the names of well nearby might be illuminating. Also, wells dry up all the time, so there's no guarantee the well even exists anymore.
