There are a lot of variable that effect the stability of aerial video. So the key is to isolate the problem before making random changes that might not have any effect on improving your footage.
Here's the order in which I suggest you check out your rig:
1. Take the props off and start up your MR on a smooth table, listen and feel for vibrations from each motor. If a motor vibrates more than the others then balance the motor.
2. Balance your props
3. remove your gimbal and hard mount a GoPro directly to your frame and run it up again without props while recording video. If there are no vibrations at any throttle seeting
4. fly it with the Gorp still attached and check the video.
5. If the GoPro footage is good, remove it and reinstall you gimbal and attach the GoPro to the gimbal if you can and test fly that. It might not be possible to balance your GoPro on your gimbal but your not looking for a level horizon buy vibration free footage.
6. if that goes well replace the GoPro with the camera you normally use and test it again.
7. if after all that you have the same result then you want to check the vibration dampening for the gimbal.
A couple of other things to keep in mind, turn off any image stabilization on the lens and on the camera. Depending on the camera and lens image stabilization can often make things worse.
Sounds like a lot to do but it usually doesn't take long. Also make sure you don't do any image stabilization on YouTube or in software, its hard to tell online but that's kind of what it looks like is causing the shuddering in your footage.
