Welcome to Nikonians, and a question is a great way to start!
I don't have a 400/3.5, but I face a similar issue with my 500/4 lens. So what I eventually worked out was using a Black Rapid R strap, connected to the tripod foot of the lens. I put the strap diagonally around my shoulder, and the lens then dangles at my waist on one side. I do need to have one hand on the lens when walking to prevent it from bumping into my body or other things, but aside from that it works very well. Also, when I use the lens hand held (on occasion), the strap stays on, and so there is no risk of dropping the lens. Finally, when I swap this lens out for another (shorter) one to take a scene picture, I can keep the lens dangling on my body side while I take the camera off.
Since I use the lens on a monopod quite often, it was not practical to screw the R strap into the tripod foot. Instead, I mounted a small RRS bracket onto the R strap, which allows me to quickly connect or disconnect the lens tripod foot, and as a side benefit, it works for the camera, too, for occasions when I use a shorter lens.