Upon reassembly, I found this easier once I was looking at the connection from the bottom of the phone, as pictured. I had been trying to line up the connector from the side. Once I put on magnifying glasses and had really good light, I lined it up and slipped my finger in for the click.
Oh, in a moment of relief after getting the cable connected, I quickly closed up the phone, forgetting to put the metal bracket covering the home button cable back on. I had to re-open the case. Don't be like me!