honestly the simplest method will be to do the trim in FCP,
and re-do your chapter markers.
starting with a copy of the original sequence, complete with chapter markers will be a help.
"If I edit the .mov in Quicktime I only know how to crop the portion I want, but I don't know how to crop out a section in the middle."
OTHERWISE
in QuickTime player, you can mark the section you want to remove with simple in / out points just like in FCP, (i for in, o for out)
then Delete will cut that section out.
JKL keys and left/right arrows for navigation also work in QT player.
this stuff does NOT work QuickTime PLayer X
im not sure if the chapter markers will move.
maybe. give it a go
when you're done you can save as either a reference move, or a self contained.
cheers,
nick