Never mind. As often happens, as soon as I posted the question, I discovered the answer.
And the answer sucks. You apparently can't do this, with PE. I just wasted my money, because I need this feature. Sigh.
Just to follow up for anyone else who might come across this issue. I found a free Mac program called "Metadata Hootenanny" at http://www.applesolutions.com/bantha/MH.html. One of the things it does is allow you to add chapter titles to any type of movie that Quicktime can read. This is not the perfect solution, but it's better than nothing.
Because QT Chapter Markers are specific to playback in QT Player, and the Chapter Markers in PrE are specific to DVD's and BD's, they will not translate - different types of Markers for different purposes, one will encounter what you observe.
Thank you for posting the 3rd party utility, that WILL apply QT Chapter Markers to your output files. That info will help others in the future.
Now, having the capability to add the QT Chapter Markers in PrE (just an additional type of Marker), would make a great feature request.