Hi,
Hard to tell exactly what is going on there. Here are a few things that you might want to try.
First, delete/reset preferences. To delete/reset preference open iMovie while holding down the Option and Command keys and select to delete preferences in the box that appears. iMovie will open in a new empty library. Reopen your old library to get back to your projects. Possibly you may need to reboot to set the changes. Deleting preferences is a safe procedure that will not cause data loss or disruption to your project.
After opening iMovie per the above, create a new project and import your clip into it as the very first clip imported into the project. Now see if the stabilization issue is resolved.
If the problem persists, put your clip on the desktop and Control-click on it to get a drop down menu. At the bottom of the menu, click on Encode Selected Video files.
Encode the file, that will give you a separate file with the original file still preserved. Now import the encoded file into iMovie and see if the stabilization problem is cured.
If still no luck, try using the stabilization feature of iMovie to stabilize the clip.
iMovie supports 4K at 30fps. If your 4K clip is other than 30fps then possibly that is causing the issue. You could try varying the speed of the clip, faster or slower, and see if that makes a difference. The easiest way to vary the speed is to control click on the clip in the timeline and, from the pop up menu, click on Show Speed Editor. That will cause a slider handle to appear in the upper right hand corner of the clip. Slide it left to speed up the cip and slide right to slow down the clip.
-- Rich