Dear Michael,
What I've found is that exporting and importing xml works best for single parts - so I would recommend exporting each part as an xml file and then including them in your lilypond score. I've even found that piano parts generally work better when each hand (and sometimes each voice/layer) is imported separately. It's a bit of a hassle - but with lilypond's architecture it actually isn't that bad. It seems to me that there is a lot of variability in how well different program export and import xml that you can't yet trust it for automatic transfer between programs. Each programs seems to miss or mess up certain things. This is true for transferring files between any two programs (try to load your file in Finale or MuseScore and you'll probably see what I mean).
Hope this helps.
All the best,
Avner