The problem that I have with my 2012 S is that when going around a bumpy corner over 50 mph the bike develops a "hinge in the middle" and starts weaving. .....
I am NOT a suspension expert by any stretch of the imagination so I can only relate your experience to my personal experience. I have a 2000 Kawaaski Concours that I used to use on long motorcycle camping trips. For those long rides, I load up both saddlebags and top case with camping gear. I also have a huge rear seat bag that gets stuffed. I put a ton of gear for those trips on my bike. If I forget to adjust the suspension, the bike develops a high speed wobble like you describe when I hit a mid corner bump.... even a slight bump. I end up cranking up the preload and rebound adjusters on the rear shock and the wobble disappears. With the bike unload for normal riding, I soften up the settings for a more comfortable ride.
Of course every bike is different and I am sure the suspension geometry has a lot to do with it but if I was in your shoes, I would do a full suspension adjust. Preload CAN be adjusted on your front forks by increasing or decreasing the size of a spacer on top of the fork springs as I do not believe that the ZERO has external preload adjusters on the forks. There are plenty of guides on how to properly adjust suspension on the internet. Either do it yourself or pay a competent suspension shop to do it for you. But I'll bet you can dial out that weave with a bit more rebound damping.
I'll bet that the issue is the rear shock's preload and damping. But I would see if I can adjust both ends so it it proper for your weight and riding style.
Also, check your steering stem bearings. With the front wheel off the ground and the bike centered, push slightly on one handlebar, let the front end drop to the steering stop. If the handlebar bounces against the steering stop, your stem bearings are loose. if it stops before hitting the steering stop, your stem bearings are too tight. Also, while the front end is off the ground, slowly turn the handle bar. It should be smooth with no rough spots. If you find a rough spot, it MIGHT be a cable (throttle or brake) or wire harness hitting something. Try and reroute the cable or wire harness so the action is smooth or temporarily disconnect the offending cable or wire harness... try turning the handlebar again... if there is still a rough spot, your stem bearings may be worn. Usually, the stem bearing wears a rough spot very near the center of the steering arc. You'll need to replace the bearings.
Form my personal experience though, a high speed wobble on bumps can usually be attributed to the rear suspension. But it never hurts to do a full suspension adjust. If none of those things fix the problem, check your swing arm bearings (remove rear shock and make sure there is minimal play and that the action is smooth). Even wheel bearings have been the culprit for a high speed wobble.
I've had a couple of bikes with the same wobble on bump issue you described and I have been able to dial it out with suspension settings or bearing preload...
Jose Soriano