I'm looking to rewire the three way switches that control the light at the top of the basement stairs and the two lights in the finished basement. Currently the power comes in at the light and is routed down to the switch at the top of the stairs. The switch at the bottom of the stairs is extended off the top switch box. Power is also extended from the top switch to the lights in the basement.

The issue is that the lights are tied into the same circuit as the living room. When the previous owner remodeled, he left it that way when he added the new basement lighting. I need to move it to a new circuit because we keep blowing the breaker. I can pull power to the lower switch and cap the power coming in at the light fixture.

I have all the wiring figured out except for one thing. The wire I have to add from the bottom switch to connect the switched power to the basement lights would have a floating neutral. Not sure if I should let both ends float or tie it off to something. I can tie one end to neutral in a junction box. But if I do that, should the other end float or be tied to neutral?

I have a drawing of the wiring setup, but I can't post it since this is my first post. Maybe if you PM me I can send it to you.