I've been trying to solve this problem with my Brompton too... I'm interested in the ideas that will come up.

So far, THIS DIY expandable box comes closest, but I prefer to travel lighter still (i.e., single front T-bag).

I think I'm going to go with the dumpster-dive approach - grab some discarded cardboard boxes, newspaper, and roll of packing tape and make a box for each flight leg (throw the remains in recycle at destination).