Well, I need the car in the morning, so I had to make a decision. After a long period of careful analysis and some discussion among myselves, I decided that little white thing to be an extraneous, unnecessary part and did some careful surgery to remove it. Everything works fine now.

As for getting the inner door handle to work... Wow! What a PITA! It was like I needed to adjust the cable a bit, but it's not adjustable.