Often deleting preferences will cure export problems. It appears that you have done that but no success.
Try exporting with Best Quality (pro res) settings. That will give you a .mov file with a different audio codec. See if that cures the sync issue.
Also, before importing the clip into iMovie try re-rendering it with the free download Handbrake to clean up any rendering or codec issues. Convert it to H.264, Mp4/AAC. Do that even if the codec already is indicated to be Mp4/AAC. Re-rendering often cures the issue.
You can get Handbrake here:
https://handbrake.fr/
A simple way to do it is to open Handbrake and do a File/Open Source. Navigate to your video and choose it as the source from the resulting screen. Then do File/Start Encoding. Wait a couple of minutes for the conversion to complete. Then save and import the converted clip into iMovie.
You can also try running through Handbrake the exported out-of-sync iMovie video.
Failing all of the above, try the workaround of re-importing the shared out movie back into iMovie and detaching the audio (Modify/Detach Audio). Then expand out your time line all the way using the slider above and to the right of the timeline. Control click on the detached audio clip and, from the pop up menu that appears, click on Show Speed Editor. That will reveal a speed adjustment slider in the upper right hand corner of the clip. Adjust the slider slightly as necessary, and reposition the audio clip until it is synced with the video. You may be able to sync it by just moving the audio clip without using the speed adjustment slider. But it you can't, then try the slider.
You can also contro-click on the video portion of the clip and adjust its speed with the speed adjustment slider, until it syncs with the audio clip.
-- Rich
