To me it makes sense that the gadgets won't work: the first step in creating a gadget is to specify its source data - the project - and in this case the project has been archived and effectively removed. The obvious solution is to restore your projects and hold them until you're ready for them to be archived. In terms of workarounds in Scale, I don't know of one that exists.
But being creative about this, as a workaround, what you could do is create a dashboard ("Archived Projects"?) that only contains gadgets for projects that are about to be archived (in your case you would need to temporarily unarchive your projects to achieve this). Once the dashboard is created it is effectively static (if the project is going to be archived the source data is not going to change). You could then take a snapshot of that dashboard and create a webpage to display it.
The projects would then be archived and your source data lost with it, but each time you are about to archive another project, you take a snapshot of that project's gadgets and update the "Archived Projects "snapshot, thus retaining historic reporting.
If none of the above helps you could try SmartBear Support for help.
