I'm sure others have come up with similar things, but I already took the pictures, so here's the little gadget I put together for about $6. It cleans 5 and 6 gallon carboys in about 20 seconds.
I think I'll add a bic pen shell or something to prevent it from banging around the neck.
The rag part is actually about 1/4 of the tendrils off of a $3 or $4 mop head replacement that I drilled out. There's a #8 (I think) nut and as wide a washer as would fit through the opening of a carboy on both sides of the mop-stuff.
Attach it to a drill and go. It does get a little wrapped up on itself once in a while, but it clears right up if you reverse the drill spin direction.