Thank you,
I read this section and tried to use those before posting to the mailing list
and it would do nothing. In the end, it was a simple case of properly RTM.
Those properties do not take numeric values but rather alists. I finally got
my score to look like pretty much like I wanted.
In the end, I used those settings :
\paper {
%annotate-spacing = ##t
markup-system-spacing = #'((basic-distance . 25) (minimum-distance .
15) (padding . 1) (stretchability . 30))
system-system-spacing = #'((basic-distance . 15) (minimum-distance .
10) (padding . 1) (stretchability . 60))
top-system-spacing = #'((basic-distance . 10) (minimum-distance .
5) (padding . 1) (stretchability . 30))
ragged-bottom = ##t
}