The absolute capper to the entertainment here was that the dialog wants to invoke a Save As dialog on the way out to let the user decide what file to save the modified contents to. If this were an actual dialog, that would be relatively simple.
However, this is actually a property sheet and there was relatively little that was simple about it. It turns out that the right place to try to patch in the call to the master Save As function is in the OnApply function for each of the property pages that make up the property sheet, because that:
Ok, that's easily fixed. First man in sets a boolean that says don't raise the Save As dialog again; add an OnSetActive override to each page to clear the boolean if/when you return to the property sheet.
I begin to see why normal people don't handle a Save As dialog this way...