Hi L.,
I just moved myself so i dont need them but if you havent found anyone there is a good website www.chicagofreecycle.com where you can place a add and I bet you will have at couple of people responding to pick them up right away.
I used this site to give away stuff I dont need anymore but i also didn't want to put them with the trash. its satisfying to know that material doesn't go to waste and that your 'trash' can be someone else his treasure.
if you need someone specific for the boxes. i have been in contact with a lady, her name is lauren and she picked up some stuff from me. i know she will be moving to new york soon and she has placed an add asking for boxes.
let me know if it doesn't work out through mamasource, i still have her email so i can forward it to you.
good luck with unpacking!
M.