Those Agrati ROMA head lugs look like the ones on the mystery Italian bike.

I think that my headset is a Record headset. Now I'm wondering if perhaps the seller has the bike's original crankset tucked away somewhere, who knows, it might be a 1st-generation Record set. I will get back to her about whether any more parts turn up, the C-Record pedals just happened to be in view when we looked in a closet for the speedplay pedal's cleats/shoes, and she will be clearing everything out of the garage this week. She also has a pair of 90's Torelli's for sale that are both too small for me. They are anniversary models painted in Italian colors, have a mid-level Campy triple group. I might offer 500 for the pair.