How can I change the settings so that my Projects and SoapUI windows stay saved

I think the Preferences > UI option only has options to save the project files or do a backup, nothing on saving the last known layout. However, if it's just the Project Properties that's getting in your way, you can turn it off from View > Properties. Uncheck it.

 You should see something like this:

The only one that will be left will be API's it's API Navigator on Views. You can do the same for other areas. For the setting, maybe you can post it in the Feature Request page if someone hasn't requested it yet.