Well, I'm all wrapped up and I feel quite good. The "only" thing left to do is patch the holes in the drywall. Thanks to everyone who's advice was so crucial. I hope I can return the favor some day (most likely in the distant future).
PS: For what it's worth, I ended up wiring it as follows:
Hot wire coming in (the old black wire in the original post) is connected to two other wires -- one goes to a standalone (illuminated -- fancy) switch and goes out to the wire that goes to the ceiling light (old red wire in original post).
The other hotwire connection goes with the incoming neutral (old white wire) the GFI outlet with the two new wires to protect the other outlet.