How do I pause my loop until text-to-speech has read every word in a string?

If you need help please provide full and clear information on what you are doing. A code snippet showing what you're trying to do is helpful as well as a clear explanation of the expected results and how they differ from the actual results. If it takes a large amount of code to reproduce the problem (several files, or more than a screen) then please share a minimal repro on your OneDrive.

That said, I'll guess that this.media is a MediaElement, in which case you can listen to the MediaElement.CurrentStateChanged property to detect when the media finishes playing.