I just now stumbled onto something that seems to work for this situation. I used the Selection Tool to replace my 2nd ending with my 1st ending. This obviously places those notes I have already tied into the 1st ending into the 2nd ending as well. Then I edit my new 2nd ending to replicate my original 2nd ending - except now, my tied notes on the downbeat are already in place, complete with ties! While this seems to work with ties, it does not seem to work with slurs, but I can live with that for now. 

The general solution for adding a Tie End to a 2nd Ending:

Speedy Entry Tool. The entry rectangle appears (probably).

Click outside the staff, to exit the entry rectangle.

Hold down Option, and click in the first measure of the 2nd Ending. The (very technical) dialog Edit Frame appears.

Select the option Tie End.

Peter Thomsen - I have tried the steps you outlined above, but the changes do not 'take' for some reason. No change appears in the score and when I go back to the Edit Frame dialog the Tie End box is unchecked.

… No change appears in the score and when I go back to the Edit Frame dialog the Tie End box is unchecked …

I am sure you realize, how difficult it can be to diagnose something blindly with nothing to look at.

However, here are some “shots in the dark”:

1) To make the Tie End work, there should be a Back Ending in the measure before the 2nd Ending.

Is there a Back Ending in the measure before the 2nd Ending?

2) To make a Tie work, the Tie must connect two notes of the same accidental/scale step.

You can not tie a G♮ to a G♯.

Make sure that the note beginning the 2nd Ending is the same as the note before the 1st Ending.

Peter - I did finally get it to work. The original setup I had was a backwards repeat preceded by an ending starting two bars before that. The two repeats were defined separately, rather than with the back ending option in the dialog box. For musical reasons I decided to go with a one measure ending and then everything worked perfectly. I just went back and created a test file with a two bar 1st ending, but this time using the back ending and then a separate ending in the measure before. It worked perfectly, so it seems like I was in violation of your 1st point. Thanks for your help.

David Case,

From your description I suspect that you have not yet discovered some convenient commands in the Repeat menu.

Personally I often use

Create First and Second Ending

Just select the measure(s) that should be played in the 1st Ending, then run the command

Create First and Second Ending

Peter - Thank you. That is much easier! I do tend to not notice the extra menus that some tools have and the repeat menu is one of the ones I missed. In future, I'll watch more carefully when selecting a tool to see if a menu appears for it.