iPhone 5s Battery
iPad Wi-Fi Display Frame
Putting the upper screws back in the bracket is a bit tricky--if you hold the screen at 90 degrees, the connector cables lift up the loose bracket, but if you lower the screen to allow the bracket to lay flat, you can't reach with a screw driver. Be very slow and patient and replace the upper left screw last (after the first three are tight)--these will hold down the bracket fairly well so you can aim the last (upper left) screw into the hole and push down as you tighten.
When you put the new battery back in, it's important to fold that tab back down along the bottom edge of the battery--do not let the tab rest on top of the battery. If you do, that minute extra thickness is enough to press ever-so-slightly on the LCD and cause the LCD to exhibit color distortion when you press the home button.
Zip tie is a brilliant suggestion. Very robust and safe way to pull the phone apart--I had mine wrapped just above the home button and kept the case from opening beyond about 1/8 of an inch.