Although it's nice to see photos of bikes that can fit all together into a single non-oversized suitcase, I wouldn't do it unless there was enough space to add adequate protection for padding and tolerance for external compression.
You have to protect your bike against these beast machines that live in their deep, dark underground lair, called the baggage system:
I've traveled a few times with my Dahon folded with the wheels still attached in the original Dahon cardboard box, but I would not recommend it. One time the latch was completely bent. I assume someone dropped the box from very high. The hinge also won't tighten completely anymore. The pin or shaft on the other side was probably bent out of alignment.
Another problem with a cardboard box is that the check in agent always made me sign a damage waiver to relieve the airline of responsibility, and I had to pay for oversize because the box was too big for standard luggage. When the box goes to the oversize drop off location, I think it gets handled differently than normal luggage, which goes through the automated system where it will meet the beast filmed in the youtube video above.
Oversized luggage probably gets handled manually instead, so it gets to the airplane slower, with a higher chance of not making connecting flights and getting delayed for several days. One time I had to wait 3 days for my bike to arrive.
Another problem with packing the bike still completely assembled is that if the container is dropped on an edge, all the weight of the bike might be pressed against a single point. Alternatively, if the bike was disassembled, each piece could theoretically hit the side of the container or each other individually.
Next time I would disassemble the bike as much as possible, wrap each part with foam padding (especially the ends), and probably pack the frame and wheels separately in 2 different suitcases. Large suitcases under the 62", 158cm linear limit are usually 50cm wide and can fit up to 20" wheels and larger frames. Medium suitcases are usually 40cm wide and can fit small frames and 16" wheels. Cheap hard side suitcases cost about $40-50 each, and the fee for checking in 2nd baggage is $25-40, if you can avoid the special sports equipment fees. At least you would avoid the $100 oversize fee. Using 2 suitcases also makes packing simpler, and would be easier for security to repack if they happen to open them for inspection.
Upon arrival, you could donate the suitcases to someone else, and after the tour is finished you could find another pair so that you won't have to return to the start to pickup an expensive custom bike case.
So I'm looking for a new bike, something that could theoretically be packed into a single standard non-oversize suitcase, and without a folding hinge at the middle of the bike that could be easily damaged. I would prefer 16" or 18" so that the wheels can fit in a more easily acquired medium suitcase. Something with a standard 8,9,10 free hub, less than $800, and strong enough for loaded touring, but I don't find many options.
Spin (chain stay design with no seat stay or bracing looks very risky, but can be completely disassembled with tools normally carried, and fits in a single suitcase with adequate space)
Tyrell IVE (could fit in a single suitcase but would be better in 2, has 18" wheels, but a bit expensive)
Birdy (really expensive, and eye candy for local theives)
Dahon Qix (maybe? not sure about the small looking pin. Probably needs 2 cases)