scheme function to align time-sig above nearest RehearsalMark?

[Adam James Wilson]

Here's a question for folks used to modifying lilypond with scheme -

In my score there is a RehearsalMark above every barline in every
staff.  I want to be able to center each TimeSignature above its
associated RehearsalMark.

I'm using TimeSignature X and Y offsets to do this now manually; for
many instances I can use the same offsets, but there are plenty of
spots the ReheasalMark moves out of the way of some markup or notes
and I have to change offsets manually.

To me the power of lilypond is being able to automate things like
this; I'm assuming I just have to get the x,y position of each
RehearsalMark and set the following timesig to these values (plus some
offset).  But I'm not sure how to do it.

Any suggestions?

Best,
Adam