RE: Purring with a diaphram...
If you're trying to go the gargling route, what you want to do is produce no sound [without a call in your mouth]. You don't want to make the gargling sound. What you do want is to vibrate your vocal chords pushing the air through your throat like you would if you were gargling.
I can't do it that way. In order to vibrate my vocal chords I have to make noise, so I can't purr that way.