More embarrassment to report here: I was looking through the ES6800 manual again, and finally did find a section where it talks about using keyboards and mice. (I don't know why I couldn't find it before.) But get this -- it apparently supports both bluetooth keyboards and mice, as well as USB keyboards and mice. So a $5 usb keyboard might just work fine.

Apparently, you can adjust the keyboard settings by going to "Menu->System->Device Manager" on the TV. (This might help getting the bluetooth keyboard working as well...)

Edit: Ah, the difference is that I'm looking at the manual for the 40 inch ES6800, not the 32 inch one. Hopefully, all the functionality in the 40 inch TV is also available in the 32 inch one...