I tried importing a project from Cloud IDE and it worked fine.
Since you had the timeout error, it might be caused by the failure to download your BIG project from the cloud. I suggest you download the project from the cloud separately, then import using “Import Local Cordova Project” option in Localkit. This will locally import the project. It should be okay in this case. Please try.
I tried with my own project and it worked fine with Localkit 2.2.1. You might have done something wrong to your project. I suggest you send a support ticket and provide a copy or more information of your project to them.
@memo Well hybrid applications run in webview on native devices - this is just how it works. We are coding HTML, JS, and CSS so as long as it runs in the browser on the device, it should run in webview within a Phonegap / Cordova wrapped application.