Reading other comments of how applying too much force caused breaking of components I was too timid and the battery removal process was very time consuming. I recommend watching the video in the battery replacement guide. I was able to see how much force was being applied to remove the battery. I found that the opposite end of the plastic removal tool was bitting into my hand, which was more sensitive to the required pressure than that applied to the components. The adhesive was quite strong and I used the point end of a spudger to gradually pry up the battery where it was most stuck at the bottom right. As useful as the comment about using the plastic tab was, mine was slightly cut by the edge of a flat cable, it split and the tab came off, making prying the battery necessary. Being mindful of the balance of force is what makes the removal successful.
While holding down on the lower sides of the iPhone, I found inserting the plastic separator just to the right of the audio jack while gently applying pressure down and back from the edge popped the bottom of the display assembly up. Keep in mind to do this while pulling back on the suction cup ring, like the guide says constant, but gentle force at the same time. Another note is to have the suction cup ring vertical to align with the length of the display, that made the process much easier.