Interesting numerology

[Fairchild]

The goal of the shtick below is to balance the two printed pages with ten
lines on each page.  As is and again by changing the fourteenth digit of
betweensystemspace from 5 to 6 gets two different results, nine lines on one
page and eleven on the other - neither the desired result.

How to control the layout differently in consecutive scores?

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\version "2.4.3"
#(set-default-paper-size "letter")
                                                STUFF = {
c1 c c c \break c c c c \break c c c c \break c c c c \break
c1 c c c \break c c c c \break c c c c \break c c c c \break
c1 c c c \break c c c c \break 
\pageBreak
                                                }%end STUFF
                                                \paper {
printpagenumber      = ##f
leftmargin           = 0.50\in
topmargin            = 0.20\in
bottommargin         = 0.20\in
footsep              = 0.01\in
betweensystempadding = -.10\in
betweensystemspace   = 1.0931579213785\in
                                                }%end paper
                                                \score {
                                        \layout {
linewidth            = 7.50\in
indent               = 0.00\in
                                        }%end layout
                                        \relative c'''' {
\STUFF
                                        }%end relative
                                                }%end score
                                                \score {
                                        \layout {
linewidth            = 4.50\in
indent               = 0.00\in
\context { \Staff minimumVerticalExtent = #'(-1.0 . 1.0) }
                                        }%end layout
                                        \relative c'' {
\STUFF
                                        }%end relative
                                                }%end score

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