(In the meantime, if anyone reads this who has dealt with Alitalia via EZ Air and has any first hand experience with them, we'd love to hear about how it went.)
We had an ITA E-Z AIR direct SFO-LHR flight about 6 months ago. I was able to book seats on the ITA website as soon as I booked E-Z Air (not ticketed). At that time I paid USD $39 pp for mid-cabin Economy Seats. There were also better location Economy seats more toward the front for USD $54 pp.
When we boarded, I was glad I paid and booked seats because boarding groups for Economy was first group those who paid $54, then next group those who paid $39, and the last Economy large group that may have been those who waited for seats to be assigned free one day before flight date.