You have the right idea about using the same circuit for the ceiling receptacle.

What kind of house do you have? If it's a ranch it would be easier to do.

Depending on how the wire is run it would be easier to shut the power off cut the wire in the basement, add a splice box, run a 12-2 from the new box up beside the stink pipe to the attic and then to the ceiling outlet. You'd have to remove the wire from the lighting circuit.

Feel free to ask any questions. Jim