After reading other posts and the answers to my own, we think we've settled on an itinerary: 2 nights in Split (we arrive late in the afternoon the first day), 3 in Hvar (from where we'll do day trips to Brac, Vis, and Korcula) and 2 in Dubrovnik.
Here's the problem: I'm still not sure how to get from Hvar to Dubrovnik. An 8-hour ferry does not appeal to me. Should we return to Split by high speed catamaran and rent a car and drive? Should we go to Korcula and overnight on the way to Dubrovnik? Help!

If you overnight in Korcula you save twice: the return to Hvar that you had built into your first draft, and the long sail to Dubrovnik is almost halved.

I'd travel on the water as much as possible, as the views are stunning.

Is it possible to do a day trip to Korcula from Dubrovnik? Does anyone know of an English site for schedules and prices of local trips on the ferry?

The only ferry from Dubrovnik to Korcula is run by Jadrolinija (www.jadrolinija.hr). There are buses from Dubrovnik which use the ferry from Orebic.
This web site has all transport connections to Korcula:
www.korcula.net/grad/pitanja/index.html
If you're going from Hvar to Dubrovnik, it really doesn't make sense to double back to Korcula: either visit Korcula en route from Hvar, or skip it.

So, is Korcula worth the visit? Or do you recommend returning to Split and driving down to Dubrovnik?

Korcula is worth the visit. You plan to visit a few places where I have been. See my report at http://www.iol.ie/~draoi/ (you need to copy & paste to get the full url).