>I want the space between one Piano staff and the next Piano staff to be the same for all variations even if a white space appears at the bottom the page.
Add a \paper block. Use the "ragged" paper
variables to disable Lilyponds vertically spreading staves. Adjust the values of "basic-distance" below as needed to define a fixed distance between staves (systems):
\paper {
ragged-bottom = ##t %disable equal vertical distribution of staves for all pages
ragged-last-bottom = ##t %disable equal vertical distribution of staves on last page only
%markup-system-spacing #'basic-distance = #12 %distance from header/title to 1st system
%top-system-spacing #'basic-distance = #15 %dist. from top to 1st system when no titles exist
system-system-spacing #'basic-distance = #26 %fixed distance between systems in staff units
}
Documentation: