How do I make the volta stretch to the beginning of the measure?
You can stop the rehearsal mark influencing the volta's spacing by overriding its X-extent property:
\once \override Score.RehearsalMark #'X-extent = #'(0 . 0)
Assuming your snippet shows where you want the coda mark printed, it's just a matter of tweaking the values in \translate:
\translate #(cons -
5.5 6.5)
Would it work if I were to remove the Coda from space calculations by \overriding the TextScript's #'extra-offset?
I doubt that would work, since #'extra-offset is applied after the spacing calculations have finished.
Regards,
Neil