Being as proficient as you are at home improvements Chris you could probably get this done right by a pro for about $250.

Naw, it's a cinch.

For that small of a gap go the tape-and-mud route.

Big ol' damp sponge to smooth, light sand, and paint.

The trick is to realize that when it looks okay STOP DINKING WITH IT.

I can't count the number of times I've had a minor problem like that solved except for the tiniest of imperfections that one can only see when literally inches from the wall - only to ruin it completely by "touching it up." And then having to re-do the whole thing.

First layer is up there. Drying. Will put up the tape and another coat tomorrow. It looks..uh..OK I'd say right now.

with that first layer up, once you get the tape on, it should be easy to add just a little mud and use the edge of your taping knife to rest on the unmudded drywall as a reference and get a good smooth line on the compound. Stick with thin coats and you can repeat in a short time to get a uniform finish quickly. Most people try to put too much on at once, and it is hard to fleather into the surroundings. Don't be shy about blending your new work way up onto the old paint, it makes it easier to get a smooth transition.
Waiting on pictures!!!