Hide SystemStartSquare if Staff is removed?

[Kyle]

I'm working on an orchestral score wherein the string parts 
play some extended passages divisi, and it makes sense to 
divide the staves during those passages. 
When they are playing in unison, I'd like to hide the second staff.
However, when the second staff is hidden, 
the SystemStartSquare is still visible. 
Simply adding 
\override StaffGroup.SystemStartSquare.transparent
to the relevant systems does not work.
It seems as though once transparency is set to ##t, it won't switch back later.
Any help is greatly appreciated.