Tonight we finished constructing the bike box and it just needs to be taped up after I stuff a few more things in there for padding.
First of all, earlier in the day I went out and bought a bunch of pipe insulation (foam padding) and some packing materials to pad the bike before we built the box around it. The picture below is a bit dark and blurry so let me describe it: A heap of bike parts with foam padding on all the sharp edges.
Then we folded the whole thing up in the two combined boxes. We used smaller (shoe) boxes to fill some of the voids between the bike and the outer box. We used a lot of tape but it is going to require a lot more! Here is our final product:
Overall I am pretty confident in our packing job but the safety of the trike all depends on how the luggage handlers treat it. If there are any luggage handlers out there reading this, please be gentile!