I thought I would share my positive experience replacing the screen on my Kindle 3, for the benefit of anyone else in a similar situation trying to decide what to do.
The background is that my Kindle's screen recently stopped displaying a strip along the top of the page (it was cracked in one corner). The Kindle was out of warranty so seeking a replacement from Amazon was not an option.
I searched for "kindle 3 replacement screen" and found a number of sources; I ended up buying one on eBay. I followed a very helpful disassembly guide found on YouTube and was able to swap the screens successfully in about an hour. You may be able to do it faster - I was just proceeding cautiously.
The only tools I needed were a very small Philips head screwdriver and a flat head screwdriver, which I used to help pry off the back cover as I did not have a "spudger" tool. The cover is held on with plastic clips around the edges, but I actually thought it was the hardest part to remove - I guess I'm just wary of snapping small plastic bits. It is helpful to have a couple small containers handy to keep the screws organized as there are two or three different sizes.
I posted a few photos, links, and more detailed comments here: anoved.net/2012/09/rekindled/