I managed to make my redemption at closing time Saturday. The wait wasn't as bad as I expected it to be; maybe 15-20 minutes.
Once you get pass this hurdle, it's just a matter of determining the availability of your desired sectors. It's highly likely you won't get what you want since nothing seems available. I didn't get my desired sectors and had to settle for forfeiting 17,000+ miles when I could've utilized all or close to all of them. Small sacrifice.
If you don't get what you want on the first try, call again (and again). I had called some hours earlier and this was the case. I kept asking the woman to check alternate dates/partner airlines and she basically barked "I have checked, sir!" So it's really the luck of the draw. Be sure to have a list of alternate sectors ready.
Alternately, you can always call again to change dates/times. That comes at no charge. A change of sector, however, carries a fee.
When you get connected to a rep, it's a good idea to ask if they speak English. Some don't and you'll have to be transferred to one in that case (more waiting).
To recap, the number in Italy is +39 06 2222. Press 3, followed by 1 (for domestic flights) and 2 (for international flights). This, for those who don't comprende italiano. It's also good if you have a cheap long-distance phone plan.
Good luck to all (for you will need it)!