Okay, making more sense now, I can see you have an option for render distance....i take it this needs to be a specific value?..can you dynamically cycle these 3 values +, ++, +++, +, ++, +++ on consecutive frames???? it would go someway to doing it.
You have obviously chosen the depth of field and DPI values carefully, if you can cycle through all the values that give a good separation you may approximate a 3D scene
You could have a seperation of half a pixel, it's just this pixel takes on 2 values over 2 consecutive frames.........
To this end you could have any fraction of a pixel within reason of frame rate, bit depth and human perception...