Hey @mgason – Welcome to the forums!
What you are describing sounds like there’s some sort of SQL file (or files) that are causing issues when importing and because of that, Local isn’t able to fully finish setting up the site.
Have you taken a look at the Local log to see if there ar any errors? If you provide your Local Log, we can take a look here as well. See this Community Forum post for instructions on how to do so:
One other thing you might try is extracting the zip file somewhere temporarily, and then try and find the main SQL file. From there, you can zip that file up with the wp-contents folder and import the newly created zip to a new site in Local. Let us know if that helps fix things, or if you find anything in the Local log!