After a few hours of calculations, I'm finally done with this (at least part 1)
Today, in the (proleptic pre-julian republican) roman calendar*, is the 3rd to the Ides of September, year 2776 AUC

*using Censorinus and Macrobius's description of modified leap year rules, with one additional rule for the long term

Also it's weekday H, aka tomorrow is nundinae (market day, ancient equivalent of Sunday)