Transposing my custom key signature

[Adam Good]

Greetings,
I searched through the list archives and didn't see much of a
discussion regarding this. Maybe one reference that it's not possible
to transpose a key signature that uses
\set Staff.keySignature =

True? If not, hopefully someone can tell me otherwise.

Thanks!

%%%%%
\version "2.12.2"

notes={
\set Staff.keySignature = #'((3 . -1/2)(6 . 1/2))
g' a bis c d e fes g
}

\relative c' {
\time 8/4
\notes
}


%%%Pitches move but Key sig does not
\transpose g c \relative c' {
\time 8/4
\notes
}