I would go the route of least evasive. First try water, then hot water, and if that doesn't work, coffee. Coffee is a mild acid that removes the toughest baked on rim char. And, if coffee doesn't work, it is most likely a flaw in the finish, so alcohol and everything you need to refinish.
Personally, I find Murphy's wood oil soap to be worthless. It stinks, it doesn't seem to get stuff off of the wood, and it stinks. And, there's just no need to use it. But, if you have your heart set on using that stinky crap... then have fun. It just blows my mind that you don't reflexively gag while using it.