Anyway, the problem was that I couldn't twist the handle. Luckily Organic Transit included the users manual for the Nuvinci Hub which has a good description and pictures showing how to replace the gear cable.
The first challenge was finding a replacement cable since the ELF has a very long cable. My local bike shop said its called a tandem shift cable but didn't have one in stock so I ordered one from Amazon.
The next challenge was figuring out how to install it. There are actually two shift cables on the Nuvinci Hub and you have to thread the cable through a hole in the handle and wind it around a guide ridge and pull it all the way through until the grommet is seated in the housing. I added some oil to the cable housing before threading the cable through to the end of the housing. There is a special clip that needs to be attached to the end of the cable which clips into the hub. The trick is to wait before trimming the cable until after all adjustments have been made.
It actually took me two tries and a second replacement cable to get it right. The first one ended up getting frayed inside the handle just like the original cable. It appears that if the cables are too loose, they come off the runners inside the handle, and get caught up in the handle mechanism. So the key is to keep both cables relatively tight. The manual says to check the cable tension by pulling on the cable housing near the handle to see how much leeway there is. Then adjust the thumb screws on the handle to keep the cable snug. I'll be sure to do that often now to avoid more broken shift cables.
Here's the pagoda I pass on my ride home. It's near the old naval hospital in Silver Spring.