I hate that job, but I just found a quicker way to do it.
I had a spool of .095 weedwacker line, and that stuff is stiff, slippery, thin, and strong.
It was easy to work a length all the way through the hem of the shorts, then tape the drawstring on the end and pull it through.
Probably all of you already know good ways to do this, but this was the easiest I've come across so far.