One way to add an additional gap is to use a 0-line staff. The gap above the strings in the Takemitsu score is sufficiently large to require two 0-line staves:
Set the minimum barline protrusion to zero spaces, change the names of the 0-line staves to one or more spaces, make their time signatures local and hide them, force duration of the first rests in these staves, set the custom scale of the rests to one and activate their ends voice property.