Hi, Jon,
It does appear that something is awry with iMovie. It should be setting the project frame rate at that of the very first video clip added to a newly created project. Apparently it is not doing that. It has to be a brand new project, as the frame rate cannot be changed once set in a previously used project.
Possibly the clip has a variable rather than a constant frame rate, and that is confusing iMovie. If that's the case, you might try running the clip through the free download, Handbrake, and render it at a constant frame rate. Post back if you don't have Handbrake.
You could also try lowering the frame rate by using the iMovie speed controls to slow down the clip.
It also would be worth a try to repeat the deleting preferences procedure, i.e, opeing iMovie while holding down the Option and Command keys and selecting to delete preferences in the box that appears. Sometimes a second try does the trick.
Another procedure would be to redownload iMovie and see if that cures it. Drag your current iMovie app from the Applications folder into the trash, but do not empty the trash. Then sign in to the online app store and access your account by clicking on your name at the bottom of the app store side bar. Your purchases will be listed, including iMovie. Redownload it from there. If for some reason the download is unsuccessful, drag your iMovie app out of the trash and place it back into the Applications folder.
-- Rich