This may or may not be useful, but I've found that the stuttering only happens for me when I shut off v-synch, still unacceptable, but I hope this might give you some relief if you have it off, turn it on.
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It can't be a vsync problem. If it is it's the weirdest one I've ever seen if you factor in all of my details about the problem. I use a 60hz monitor so I have to have vsync on no matter whator it will screen tear like crazy. Trying vsync off anyway to test it, it made the stuttering way worse and of course introduced bad screen tearing. I know what you are saying though. When I play Overwatch there is a 5ms response time on my monitor so I can notice a very slight input lag on screen but only very slight. Vsync off fixes it but of course gives real bad screen tearing on a 60hz monitor. *side note: btw you will find people all day that say a monitor response time has nothing to do with input lag but I can directly confirm that it does. Before this 5ms 32" monitor I had a 39" hdtv that was a 30ms response time and the input delay on the mouse input was horrific. 5ms is much much much less noticeable. My monitor also has 3 response time settings: normal, fast, and fastest. Fastest feels like next to 0ms response time but introduces bad image ghosting. Normal setting is too noticeable input delay so I keep it right in the middle on 'fast' where ghosting is minimal and not noticeable while in the action and the input elay is so minimal it is almost non existent.
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You're probably lucky enough to not notice micro-stutter. V-sync also stutters after a period of time spent in public events. I would bet that everyone has stuttering regardless of vsync / rig /fps. Multiple people here, technologically literate enough to test the game on every relevant driver and setting, on top-tier i7 rigs and 10XX GPUs are reporting the same exact problem.