holy toledo, batman! I finally, many, many hours later, figured it out!
The answer for those who may be interested -
This was again CSS code that needed to be added. In the strip_example.html code I found this:
#flashcontent {
width: 100%;
height: 440px;
}
Originally it was 400, I experimented a little with different numbers and found that 440 worked just right for my page.
I was just about ready to give up and go to bed.... but took a break, thought about it some more and knew there had to be a clue somewhere in the examples. Then after comparing the code in the different html files, I had my breakthrough.
Pretty satisfying! I now have my page exactly the way I want!
Thank you Felix for creating AutoPlayer!