I'd like to be able to drop specific users into a custom dashboard WITHOUT modifying the defaults for e.g. the Search app. Also I don't want to have to make an entire copy of the Search app just to do this.
How can I go about this? Is it a Request For Enhancement maybe?
You don't have to copy the search app. Most of the share-worthy views in the search app (flashtimeline, charting, etc) are already global and therefore available in all apps. You would need simply need a new nav for your app that defaulted to your chosen custom view, which could also reside in that app. You can then set the default app for your user to this new app.
The one view that's not exported to the system space is the dashboard view, ie "all indexed data". So you'd have to either copy or export that view yourself.