I managed to fit my Mini into a Samsonite Oyster for my impending trip to Africa. I did some minor disassembly:
Removed handlepost from fork
Removed handlebars from stem
Removed front wheel
removed pedals and put them in reverse
unhooked brake cables (not essential)
I see the saddle and seatpost might have stayed fully down. I didn't try it. In the pic it is tucked through the stand under the BB shell.
It is a tight fit and I deflated the tyres to get some extra give. But at least I didn't have to remove the back wheel - just the nuts are loosened to allow the wheel to go forward a bit.