Hi,
the between-system-padding value doesn't seem to work if more than one
score block is present. Is there any way to enforce this value to be
taken into account on formatting for both score blocks?
The extra score block is a red herring: Lilypond uses 2 different values for padding: it uses page-breaking-between-system-padding while it calculates where to put the page breaks and between-system-padding when it decides where to actually place the systems. But if you set between-system-padding to something huge without modifying page-breaking-between-system-padding then the page-breaker will put too many systems on a page. When it comes to actually positioning the systems, they end up sticking out the bottom of the page and we need to ignore between-system-padding to compensate. I suppose we should print a warning in this case instead of just ignoring it silently.
In any case, you should generally set page-breaking-between-system-padding to something close to between-system-padding.