We used both top box and roll bags on our trip. We used bungees everywhere.
However, we stopped off at a BM dealer on the way and they gave us a bunch of nylon straps, a little like the straps you have on rucksacks, with a metal spring loaded catch. I think thesea are the ones that come with new bikes in the crates to secure all the loose bits before the bikes are assembled at the showroom.
Feed the tab through the catch and pull tight, job done. Very strong and did not slip.
Best bit was that they were free!
Adventure: it's an experience, not a style!
(so ride what you like, but ride it somewhere new!)