I'm going to go ahead and close this issue as it turns out that the problem isn't that the button events aren't firing -they are, but I seem to lose the handle to the dialog and can't grab it to close. Obtaining the div that encloses it doesn't seem to work, nor does obtaining the generic $(".ui-dialog") and calling .dialog('close') on that. If I could just figure out what the dialog's "X" button is using and reverse engineer that...
I'll open up a separate issue for tha problem.