I wouldn't pull much more of a trailer with a KLR then the one in the first video in post #2. I pull a two wheel camping trailer all the time with my Goldwing. It is a little over 400 lbs. dry. With full gear, I have had it at 600 lbs. You just need to remember that it is back there and plan out your stops sooner. When stopping, you know it is back there pushing on you. The brakes on a KLR are fine for just the bike and rider. Add more weight, with the trailer, and the brakes are marginal at that point unless you start slowing sooner. You will also feel it back there when going over bumps. The trailer pulls on the bike when going over bumps. But, with a small single track like the one shown, it will be better than a two wheel trailer.
Unless you are thinking of getting big things at the store, a removable top box would work better. That is what I use and I can get a lot in there. Need more room, add some side boxes.