Update from me:
They emailed me on Mar. 15th offering a 70% tuition waiver. That's a great thing, but I'm still weighing it against full tuition offers at US schools. Biggest downside for me is salary coming out - it's just much higher in the US. I already have ~$25k of student debt, and moving the family (wife and 3yo boy) to Europe would be expensive - more debt. So as cool as it would be to work in Italy, I don't know if it makes financial sense.
Not complaining, since it's a great decision to have to make

They've given me until Mar. 22 to put down the initial fee (still 10k euro), so I'll update when I've decided. Wish me luck.