Combining separate MIDI track lanes with drum maps should not be a problem; I do it all the time.
Dropped MIDI notes usually means the MIDI Prepare Using Buffer is too low (the pre-X1 default of 500ms is recommended; the more recent default of 250ms is too low in a lot of cases), but this only affects real-time rendering; if you're using Fast Bounce, it shouldn't be a problem.
I can't imagine what would cause parts to render at the completely wrong time, unless you're exporting a limited selection, and not selecting all the way back to time zero.
Other than that, I would suspect maybe a problem with a specific drum synth. What synth are you using?