If your phone is rebooting every few minutes, the replacement battery is a dud
15 minuten - 1 uur
Sometime during the summer, the phone suddenly started shutting down at about 40% pretty frequently. Resets, battery cycling etc were unsuccessful in restoring reliable functionality.
The first battery sent to me was a dud. iFixit shipped a second one immediately, but still a royal PITA and caused me to have to take the phone apart about 5x instead of just 1x.
One way to know a dud battery—the phone reboots every few minutes. As such, I wouldn't push the case completely shut until you've let the phone run for about 10 minutes successfully. (You can't use the Home button while it's open btw.)
Honestly, if your phone battery comes unstuck pretty easily, I would NOT remove the display. There's three more fiddly screws to get back in (one of which was aluminum and therefore impervious to the magnetic screwdriver) and once I managed to crimp the display cable slightly causing a yellowish spot on my display until I redid everything.
Before you remove the display, try gently prying the battery out with the display at about a 70° open angle. If it comes out, then just drop the new one in and you're two screws away from being good to go.
It's maybe a little more tricky/risky to do it this way, but OTOH you don't have to bend the display cable quite as much if you're successful—gotta get really close to 90° open to reach those 3 display cable screws with the supplied screwdriver.