I don't have experience with the 3T Aura specifically, but the tools I've found useful are:

1) Jury rigged wire with a little u-shaped bend on the end to try to grab and hold the wire from the other end and guide it along.
2) Strong magnets. You can grab the cable through the carbon with the magnet and guide it toward the exit port. (doesn't work on all brake cables since some stainless steel is non-magnetic)
3) Vicious, brutal profanity, liberally directed at various inanimate objects.

I think i have resorted to #3... i bet if i did this drunk i would already have it done

coat hangers... straightened out is usually easier.... I try and get the end of the coat hanger wire to jam into the end of the cable coming form opposite ends then flex the cable back toward the hanger hole keeping pressure on the cable and using the wire to guide it out the hole.....

Its a prick tho....

Also its not uncommon for the exit hole to have less than perfect finish (aint that the truth!!) but back to bars... a round file can help smooth the inside face to remove any hang ups which seem to catch the lip of the cable just as your getting it up to the exit hole....

Best of luck..

Ok... so for anyone that wants to know what finally did it... You know the bread ties that close up the bread... (well that is until you lose it and spin the loaf and tuck the end under the bread). Home depot in the picture hanging area has that stuff in a spool. I was able to fish it through with the weedeater line... then strip off everything down to the tiny wire. Used a fishing trick i learned long ago when using wire line and wrapped it... pulled it through.. worked like a charm!