Coincidentally, the next day my friend Roo tweeted that he'd dropped his Kobo and broken the screen. I suspected that between the two of us we probably had enough parts to build a working Kobo, so I arranged to collect his e-reader so I could try to rebuild one.
The Kobo is fairly simple inside. The e-ink screen is mounted on the circuit board and connected to it with a flexible flat cable which wraps over the right-hand side of the board to a plug on the reverse. There's a lithium-polymer battery in the lower left hand corner, and you can see the 5 buttons of the rubber navigation pad in the lower right corner.
First, unplug the flexible connector, but be careful! The plug has a plastic clamp to hold the connector in place. These break easily and without the clamp you'll get a poor connection. You need to disconnect this so that you can have unobstructed access to the edge of the screen.
I found that a thin utility blade slipped easily between the screen and the board. Just run this around all four edges and you'll loosen the tape. The tape will re-adhere pretty quickly, but it's quite easy to pry the screen off with your fingers once you've cut through the tape.
After swapping the Micro-SD cards the new Kobo showed all of my books in my library, but would only let me read some of them. This suggests that the DRM scheme is tied to some serial number on the device, and also that not all books are protected by DRM. I did a factory reset on the Kobo, connected it to my laptop and resynced all of my books. This made all the books readable again.