I realize that in my vapors, I was not totally clear about the map above. Here is some context:
Rome/Milan: 2 hrs 45 mins, 389 miles
Rome/Genoa: 5 hrs 22 mins, 326 miles
Genoa/France-Italy border: 3 hrs 40 mins, 100 miles, compare to:
Rome/Venice: 3 hrs 30 mins, 352 miles
Via Genoa, takes me 9 hours to get from Rome to the border. This does not include the mandatory 2-hour stopover in Genoa due to the fact that the earliest train I can take from Rome gets me into Genoa 3 minutes after the previous train leaves for the border.