You seem to use the same technique that I use to play pinches, I find that holding the pick tightly and picking at an angle presents a little edge of skin which makes the harmonic. Because the thumb edge makes a very thin contact (because of the angle the thumb moves across the string) it does not mute the harmonic and a roughly similar technique can be used for upstrokes and downstrokes.
I often change the angle of my pick when I play, I have a circular action to what I play, dragging the pick down strings and then dragging it over the strings on the way up again. I also use a very heavy plectrum, if I was to play without this dragging motion I'd probably break strings.