Morphing edge drawing (MED), a graph drawing technique, is a dynamic extension of partial edge drawing (PED), where partially drawn edges (stubs) are repeatedly stretched and shrunk by morphing. Previous experimental evaluations have shown that the reading time with MED may be shorter than that with PED. The morphing scheduling method limits visual clutter by avoiding crossings between stubs. However, as the number of intersections increases, the overall morphing cycle tends to lengthen in this method, which is likely to have a negative effect on the reading time. In this paper, improved scheduling methods are presented to address this issue. The first method shortens the duration of a single cycle by overlapping a part of the current cycle with the succeeding one. The second method duplicates every morph by the allowable number of times in one cycle. The third method permits a specific number of simultaneous crossings per edge. The effective performances of these methods are demonstrated through experimental evaluations.