Lining up notes in staves with different rhythms and time signatures

[Jack Taylor]

Hi all,

I'm new to Lilypond, and I appear to have chosen a fiendishly difficult task
for my first score. It's an example for an academic paper written in LaTeX
with lilypond-book. I'm trying to input this scanned music snippet
<http://i.imgur.com/npBqY1V.jpg> - a comparison of two Hungarian folk songs
- into Lilypond to have it properly typeset. The problem is that the notes
in the two songs need to line up with each other, but the time signatures
and rhythms are completely different.

I have managed to make the time signatures for each song independent, but
I'm having problems making the notes line up (and with stopping the music
from running off the page). I've dumped my current code at PasteBin
<http://pastebin.com/Z6kmy6yt> if you want to inspect it (it's not very long).

This code produces output that looks like this.
<http://i.imgur.com/ITCV26K.jpg> I have tried to investigate ways of making
the notes line up, but a journey into the depths of the learning manual,
notation reference and internals reference has left me a little cross-eyed.
Could anyone give me some pointers on the best way to proceed?

Best,
Jack Taylor