piano - crossing staff stems

[Matt Jibson]

I'm trying to write out some music in lilypond, but I can't figure out 
how to correctly cross the stems. Here is what I have as output:
http://www.crescentisland.com/lily/petrouchka.pdf
but I want: http://www.crescentisland.com/lily/clip1.png
(.ly file used is at: http://www.crescentisland.com/lily/petrouchka.ly)

I looked at the Schumann Romance in from the examples, since it also has 
three staves and crossing. I attempted to duplicate it in a number of 
ways, but failed. At one point I had four note variables for three 
stems, and combined two of them in one staff (just like righta and 
rightb are in the Romance), but I got an error about too many clashing 
notecolumns. How can I get something like what is shown in clip1.png? 
Thanks.

-Matt