The simple answer is to leave the old wire in place but disconnected at
each end. And if you are being kind to someone who comes after you then
both ends can be labeled neatly. Then you run new wire in the easiest
way which is safe and code-compliant.
If you are dealing with an unfinished basement then coming up from there
has always seemed the easiest way to manage outlets to me. An unfinished
attic has always seemed easiest for ceiling fixtures.
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