This is what i have been doing for almost four years.
http://linustechtips.com/main/topic/165643-flying-with-a-desktop/?p=2205161
Buy another case, same or cheaper and just rebuild the system on the other side. For monitor, i would just buy another monitor on the other side and leave it there.
I recommend not bringing too many unnecessary things for show if you are flying back and forth very often.