I would like there to be more vertical space between the staves.
I am totally lost on this so I didn't know what to try. Sorry.
Look here for documentation on this. The property your are interested in is system-system-spacing
. My \paper
block looks like this (adjust to taste):
\paper {
system-system-spacing =
#'((basic-distance . 8)
(minimum-distance . 4)
(padding . 2)
(stretchability . 60)) % defaults: 12, 8, 1, 60
}