Actioncam to gimbal adapter (Yi 4k+ to Zhiyun Smooth 4)

I own a Zhiyun Smooth 4 gimbal, which is made to stabilize videos taken with a Smartphone camera. It does a very good job in doing that, but I'd like to use it with my wide angle 4K-resolution Yi 4k+ action camera, to record running videos for winter use on the TV in front of my treadmill.

The Yi 4k+ has excellent build in video stabilization, but when running the camera tilting angle changes simply too much for the image sensor to get sufficient picture information. So the combination with