Hi!

Anyone know of a device that is sort of a hard drive enclosure that will let you insert CF or SD cards and dump their contents onto the drive allowing you to keep shooting?

Yes. Nexto makes several of them.

I have this one:
Nexto DI Nexto eXtreme (500GB) ND270500G B&H Photo Video

If you need to use SDXC media, pay attention to what the particular model supports.... not all support that yet.

I use a Hyperdrive 250gb
The Hyperdrive Color is also UDMA and very fast.

Sanho HyperDrive COLORSPACE UDMA SHDCSUDMA250 B&H Photo Video

Take a look at the new Nexto DI 1501. Backs up a 32GB CF card in under 8 minutes. A 2.4" LCD low res viewer allows you to see your clips to confirm capture. You can also do a bit-by-bit verification to confirm that all of the data from the memory card had been transferred to the internal HDD of the Nexto 1501.

The Nexto DI NVS 1501 comes with either 500GB or 750GB of storage.. Firewire 800 & USB 2.0 connectivity. Available at B&H, Abel Cine and other dealers.

hope that helps...