I do NOT recommend leaving the display and the rear case connected during this repair. If you run into any resistance removing the battery, or slip in the least removing it, you WILL tear the ribbon cables that attach the two pieces. I did and now I've got to replace the Front Camera and Sensor Cable. MUCH Sadness.
for anyone doing this for the first time, definitely detach the camera/screen before trying to remove the battery. it became a real tug of war to get it out. battery can get mangled/bent. Be sure to reconnect before the final battery attachment. bending the battery connection before reconnecting was key.