I'd totally be up for an independent Rhineland, with Köln/Cologne as our capital. Just keep open the borders - I still want to visit Lower Saxony and all our Western neighbors, after all.
Helgoland, that would cause a whole bunch of problems, like the fact that when people flee a place because they're in danger, they don't really want to spend 6 month waiting for the embassy to process the paperwork. Also, international law force us to accept legitimate refugees when they show up. Finally, having done some activism related to refugees in Belgium, I don't trust our asylum institution (whose main goal seems to send as many people back as possible to please xenophobic voters) so I prefer to have them operate closer, where activists and human right lawyers can more effectively monitor them.
Having such refugee processing done in North Africa (where you already have camps full of wannabee migrants) I could be okay with though.
They'd have to flee into neighboring regions first, anyway, so they could presumably apply there. But you may have a point: Embassies in unimportant (from our perspective of course, eurocentrism ho!) countries may simply be too small. How about a couple of major 'collection points' in various regions? These could then be monitored independently and effectively.
I don't quite understand the bit about legitimate refugees - we do accept them, after all, if they conform to our procedure. So they'd probably be shipped back to Africa immediately and the politely shown the nearest of our immigration institutions.