A thousand roads lead men to Rome

I want to have one of my characters in AD 11055 discovering that the only language he has in common with the posthuman self-aware machinery covering the earth from pole to pole is Latin say to himself “All roads lead men forever to Rome.”

What is the correct grammatical way to say this? My untutored guess is

Omnes via ducunt homines per saecula Romam

— but if any of ya’ll Latin scholars out there can help me not embarrass myself before I go to press, I’d be grateful.