I started using big Nikon lenses several years ago with a 200-400 f4 V1 on a D200.
For my dismay I couldn't get anything that I liked, so started to wonder if they deserve such a grand...
Later I realize it was a focus problem, then a shutter speed one and then I looked at my tripod/head combos. It was a learning curve with lots of ups and downs; until I decide to sell it… shouldn’t have done…
Today if I look at the long lenses array in my possession, I see that the better I can control the externals the better the photos, which means never had a real issue with mines. I currently shoot the 200f2 and the 400f2.8FL. Had “all” of them, the 300f2.8, 500f4, 600f4 and 800f5.6 AIS. All of those served me well with no issues at all, and man, some have withstood harsh environments.
The outstanding quality of the new 400 allow me to have 3 long lenses in a smaller and lighter package, than ever before, which includes the new versions of both 1.4 and 2x TCs. Is incredible the IQ at 800 f5.6 (400+2xTC). At that 400FL wide open is breathtaking… And I’m also using a D810, and a D4s as well.
That said I don’t believe the problem is within the lenses, but being bought used it’s hard to tell how they have been treated.
Regarding the ones you have, the 400 is a different animal comparative to the 500. The 500f4 VR is not an easy lens to get perfect shots. It seems so, but suspects you and treats it as a bigger one. It really needs a stronger than expected support. From all that I had it was the most difficult one to handle, even the 800 AIS was easier to shoot.
Other thing that I found with the old ones vs the new ones was they need to be fine-tuned, with or without TCs. The 500 f4 (many will say differently) don’t like TCs. The 400 yes, all!
Look at your D810, because it could be the culprit...
But if you still have that bad feeling send those to the nearest Nikon to get them serviced. They deserve!