Flugelbinder;
Have a look at this article. It might give you some added context to what is happening with your autofocus. The article is 4 parts long.
LensRentals.com - Autofocus Reality Part 1: Center-Point, Single-Shot Accuracy
All PDAF cameras when used with lens with fast aperature wide open need to have some micro focus adjust. Unless you are very very lucky out of the box. Some combinations work better than others.
What may be worth ruminating on would be what is the variation inherent with the screw drive system - I suspect that the screw drive is more accurate than a third party in lens drive (for many reasons) and more reliable than the SDM system. But I think one of Roger's key findings in his fourth article is particularly interesting:
" Older cameras don't have accurate enough AF sensors to take advantage of the new lenses' capabilities. Older lenses can't move their focusing elements with enough accuracy to take advantage of the new cameras' accurate sensors."
I would say that the 35 f2.4 falls into the second sentence. Although its not particularly old (2010 roughly) its plastic construction largely and not quite the same precision lens as a Limited lens in the same rough focal area. Although the 35 f2.4 uses screw drive it likely has less precision (more slop) in its drive assembly than does say a 35 f2.8 Limited or 40 f2.8 Limited. And at narrow DOF i.e. wide open it won't take much lack of precision in the drive assembly to lack repeatability.
So what does this mean? You have a camera body with an f2,8 cross type sensor and you are using spot. You lens is showing variation you don't want and can't correct for reliably. So get a better lens. Its very likely not the body.