i had to ship some systems to Canada via airline.
i put a piece of plywood over the LCD monitor; that went in a briefcase.
and got there in one piece. of course i had to take off the pedestal, so.
overall it sounds like a good job for a suitcase. e.g. a softbody suitcase
with a few pillows, or a hardbody suitcase that is just plain bigger than
the desktop case.
for some hardware i save the original shipping box for just this reason.
tie a rope around & fashion a handle & you're done.