Well, I finally got a DVD burned that works the way I need it to when played on a TV. Here is what I did: I created a temporary menu at the bottom and then dragged all of the items off of the main menu onto the temporary one, leaving my "play all movies" button on the first menu. (I also discovered that if you move everything off of a menu, then MyDVD throws away the menu, so you have to leave one thing on it.) Then I proceeded to drag the items from the temporary menu back onto the main menu in the correct order. I then burned the DVD to test on the TV.
While it may be tied up in the functionality of the particular DVD player, the first item on the menu (the play all movies) proceeded to play as soon as the DVD was loaded into the machine (rather than the menu), but this was ok. I was able to use the top menu button on the remote and get back to the menu. Further, I was able to reach the "play all movies" button individually, which is what I set out to do. I did notice that using the DVD player remote arrow keys to move around the menu still seems to produce somewhat erratic behavior, but I could still get to each item via some combination of arrows. So I finally have my objective achieved.
A couple of things: note that the movies in the "play all movies" button follow the order on the edit/movies menu. So if you go back later and correct something in one of the movies and then re-add it to the project, it goes at the bottom of the movie list and you have to use the move up/down buttons to get it back into the right place, that is, if the sequence of playing all the movies is important. I was also careful not to have any other programs running in background when I burned the DVD, and also to have the disc defragmented as was suggested in a previous post. I don't know if this is still vital once the movies were created in VW rather than MyDVD, but, trusting no-one, I still ensured this state of the environment. Following all of these rather obscure rules, I did get everything to work out OK and I now know what to do in the future.
Once again, a big THANK YOU to everyone who helped me through this learning process.