The jack connects to the phone via the contacts you can see on its topside in the picture (to matching contacts on the motherboard). There is nothing delicate or electrical underneath it; the jack assembly is just a separate piece taped with the double-sided phone tape to the frame. So there is no need to be super gentle on this step.

In English: it is easier work your way around the inside of the battery compartment rather than around the outside. Also, the clip below the power button (i.e., top of the battery compartment) will release the whole top edge.

Screen was loose, now fixed in 20 minutes, going to step 7. Yay! Rockstars.

I soaked the back of my camera, which fried the LCD and one of the buttons. Bought a new back on eBay for $60 and used this to replace it in about an hour. This might be the preferred way to replace the LCD for some folks, to avoid having to what appears to be a fairly delicate desolder-resolder to replace only the LCD. As of the time of this comment, the parts cost a little bit more -- like $20 for LCD vs $60 for the full back, but not prohibitively so.

To isaac: no. The exterior glass is separate from the LCD.