**Note during this step how the cable flexes. With the new battery you will need to carefully bend your new connector to be able to flex in the same way, which is easier to do before you install the battery. in fact, i agree with other comments that for re-install it is easier carefully hold the battery up a bit (to keep it off the trackpad components), and install the plug as you are moving the battery up into place. This will limit the amount the cable needs to flex and take that pressure off the connector to the logic board.
Seriously consider the isclack. I have a lot of experience working with much more valuable equipment than a phone, and I had read all the precautions... but I broke the cable anyways. The isclack is specifically designed to open the phone but only wide enough to get the clips out, while saving your home button cable.