Ah yes. There's a lower point on the cable where you're already in an elliptical orbit with the perigee at the altitude you want. For a target orbit of 400km,

Ah yes. There's a lower point on the cable where you're already in an elliptical orbit with the perigee at the altitude you want. For a target orbit of 400km, that happens at about 23.8Mm, 57% of the way up the cable. At that point you just have to let go of the cable and you'll only need a circularizing burn when you reach 400km: Δv of ~2,137m/s. This is not taking into account the further savings from aerobraking as I don't know how to calculate that.