My Fischer Random Dice System

Hi everyone!  I wanted a dice solution to randomly select a Fischer Random opening setup.  One could use an app or computer to select a starting position, but where's the fun in that?  I wanted it to be done in a single throw of dice (no rerolling dice over and over) and to not have to refer back to an index to setup the board.  (i.e. no dice roll from 0 to 959 and then referencing a table of starting postions)  Here's what I came up with:

*All back rank starting squares numbered from left to right

1) Use the white d4 to place the LSB on the Nth light square

2) Use the black d4 to place the DSB on the Nth dark square

3) Use the red d6 to place a knight on the Nth remaining open square

4) Use the red d5 to place a knight on the Nth remaining open square

5) Use the green d4 to place the queen on the Nth remaining open square

6) Finally, the remaining three open squares are occupied the the two rooks and the king, with the king always going in the middle.

What do you think of my system?

People will still complain because supposedly not all positions are equal in evaluation.

Why not just let the players decide where they want to shuffle the pieces and then play that way? Why do they have to be symmetrical?

The whole point of fischer random is to eliminate opening preparation.  Choosing the starting squares is fine, but that's a different game than FR at that point.  I wanted a dice system to randomize the back rank.

You're just throwing the ball out further, but there still is order. If we said it wasn't symmetrical it could be more random. Perhaps they don't  do this because then one side could have a terrible start compared to their opponent. 

If you are trying to get complete randomness, then why not set it up so there is an equal evaluation with randomly placing the pieces on the first 2 or 3 ranks? If you don't like the idea of having any pawns on the first rank then move it to 3. Like this (only an example, I am not sure how valid it would be).