<Snipped quote by Dinh AaronMk>
Any other way of giving the Republican Empire the imperfect knowledge of the old days needed to form their nation, then?
You wouldn't really need any knowledge of the old world to form a republic, tbh. If anything, where a feudal state may be said to be when an individual acquires so much material power he can influence or subjugate others to form his dynastic state, the process of a Republic is when a collection of people acquire material wealth giving them power, but not enough to really over-power one or the other; and so might confederate to form a Republic among themselves.
Otherwise, it may be little more than survivors trying to form a semblance of normalcy by re-establishing what was lost to manage their stuff. They wouldn't have to know how the Republic of Rome or anyone went about it. The Romans themselves didn't really have a book about how to set up their Republic, and they themselves were a vague silhouette of a Republic to the American Founding Fathers who only had vague notions of what they were doing.