The part splits out temporarily into divisi parts on multiple staffs. I always have trouble getting the correct incantations to get the correct result.
I can get a pair of staffs that are correct on their own by creating a StaffGroup with two new staffs -- http://lilybin.com/1l8whf/9 -- but the original staff continues through. Omitting the explicit \new Staff invocations doesn't help -- http://lilybin.com/1l8whf/11.