i had the same obsession with those tiny little flecks of dust bugging me and staring at me, watching my every move, never getting out of my brain...uh, let me take my meds...
...ok, so anyhow, i decided to take out the screen and wipe it gently with a micro fiber cloth but that introduced even more insidious flecks of deceit, etc. so, i soaked the screen in a few drops of glass cleaner and prepared a low dust, low static "clean room" using the bathroom and ran the shower for a bit to raise humidity and quell the dust then opened the cam and replaced the rinsed and air dried screen. Success! The screen was perfectly clean, i mean not a visible speck of dust anywhere on it. then, while shooting the next day, my screen came loose in the camera and banged around on the mirror and received a significant scratch near the perimeter. apparently, i failed to secure the little latch just right and it popped open.
the scratch is a big black streak...watching me...but still no dust.