I would totally dig a warforged-awakening Last War campaign.
I think I would prefer to move the timeline back a bit, closer to when sentient warforged were first introduced. The current proposal (though only one person has presented a time period so far) is ~2-3 years before the Day of Mourning, which puts it at ~991-992 YK. The first sentient 'forged was made in 965 YK, about 25 years earlier. I propose the campaign start around 970 or 975 YK, giving enough time for the replication of sentient 'forged on a wider front, but not so widespread as to be totally common.
The PCs could, perhaps, be the first entire unit of sentient warforged, at least in Cyre.