I already built this and am working on my 2nd trailer with the same cargo box you have.
Yes my dog does ride in the box. He heads to my hideout in the mountains with me. I used a longer piece of tubing for the tongue, it is supposed to reduce sway.
On the second one I am working on I will try the factory tongue but I am going to narrow the bed and axle of the trailer a bit.
The only time I notice it is if I don't accelerate completely through a turn. You can feel it want to push the bike a bit. It's a good reminder to accelerate through turns.
Many trips to the mountains with it and this summer my boy and I went from Va. Beach to Yellowstone with it. Overall I feel it is much safer than the sidecar rig I had was. It also has the benefit that I can unhook it and be free.
Minimal change in mpg on the FJR, Highway mpg went from roughly 42 mpg to 25mpg with the hack.
On the HF trailer make sure you pull the bearings out and clean all the cheap chinese grease out and pack them with something quality.