Aux output strips away the system and master effects. So when you send PART output to Assign L&R - these two levels of effects are stripped away. Not a perfect "mirror".

You can, however, do the following - assuming you are not using A/D Inputs:

1) Route Main L&R audio cables (unbalanced 1/4" TS) from Main L&R outputs to A/D inputs L&R.
2) Change Common/Audio A/D input routing to output to Assign L&R.
3) Make sure A/D input insertion effects are turned "off" (thru). Just for grins - you can set reverb/var send to 0 - although not really needed for the purpose of Assign L&R.

Now your Main L&R and Assign L&R will be mirrors of each other.

This "ties up" your Main L&R. This can be solved by using a mixer with two sends. One send would go on to external speakers/gear and the other send would "loop back" to A/D Input as suggested above.