All very interesting and possibly helpful comments.
I had a terrible, bona fide tankslapper on a 2000 BMW R1100R and did not crash. The bars were slamming from stop to stop, I was hanging on for dear life, the insides of my ankles were seriously bruised because my feet were not on the pegs, my body was being rag-dolled and legs hammered against the bike with each slam. After a few slams, miraculousy the bike straightened out and I regained control. I had really dialed up the power cranked over out of about a 45 mph turn and the back end came way out, nearly high-sided but ended up in the tankslapper. I could hear the front tire squealing at every lock and went back to see several black streaks on the road. Taught me not to whack the throttle while leaned way over when uncertain of traction; there was a bit of sand and the corner was in shadow and I couldn't see it.
That bike comes standard with a steering damper and it didn't prevent anything. Later on the damper blew a seal.
The ZX-10R as we all know is a 170+ HP superbike and it will darn well headshake and tankslap. Any bike of this type will do this, it's a light bike with huge power, a serious combination. I don't claim to be the world's most aggressive rider because I would like to get home at the end of each ride or track day but I promise you, this bike will headshake HARD if you are hard on the gas and catch a crack or rut in the road that happens to knock the tire a certain way. There is no way to completely dial out that tendency. That is why they call these "superbikes". Sure, being a good, smooth rider will help, getting the Ohlins SCU is a great idea, but to eliminate them altogether? Keep your power mode on minimum and traction control on maximum and ride like an 80-year-old grandma. Better yet trade your Ninja in and get one of these: