Thanks, Clay! That did indeed work.
I set <window modal="true"...
I called window_show(myxuiwin, 1);
I called event_process(0);
And then, as you suggested, on every button, ESC, or , the first thing I do is call:
event_stop_process(0)
The 0 is significant. If you provide a non-zero value, all input is suspended and the dialog itself is not accessible to the user until the ESC and then the dialog is available but not modal. Also, if you do the window_show() and event_process() timing wrong, very strange things happen.