If necessary you can resort to manually adjusting the control points of a slur. This example demonstrates the use of \vshape, visualizing the control points as an aid to adjust the slur's shape. After the adjustment is done, simply replace \vshape with \shape.
The \shape command also supports shaping of slurs broken by a line break, which is explained in LilyPond's Notation reference.
Adjusting slurs with \shape should be the last editing step; there are high chances that layout changes also alter the shape of slurs.