LilyPond - dynamics and MIDI output

[Ed Ravin]

In piano music, the dynamics written between the upper and lower
staves seem to apply to both staves.  But in LilyPond's MIDI output,
the dynamics are understandably only placed in the staff where they
were entered.  When the MIDI plays, one staff gets louder and softer
in the right places, while the other plays at the same volume throughout.

I know that LilyPond's main purpose is music typesetting, with the MIDI
output a secondary function, but is there any way to deal with this?
Maybe write the dynamics in a second time on the lower staff and make
them all invisible somehow?