It depends what you mean by the "modern Central Italian cluster". Geographically, Tuscans may be in Central Italy, but they are pretty close to Northern Italians like the people of Emilia/Romagna and Liguria.
The Abruzzi are in central Italy but they are Southern Italians genetically and linguistically.
Modern Lazio itself doesn't have many real, authentic, "Central Italians" left, but generally speaking, anything south of the environs of Rome itself is southern Italy, mostly because of re-partitioning of the provinces which added parts of Campania to Lazio.
Hopefully, Pax will respond, but I would say you'd be looking at Umbria, Marche, northern Lazio, and you might want to include Toscana.
I can't speak to Umbria, the Marche, northern Lazio, because there are no academic samples for them, but we have a lot of academic samples for Toscana, and it runs about 25-30% ancestry from Yamnaya, depending on the study. However, that's the total for all sources, all time periods. (Bergamo is 33% I think, and the south somewhere around 20-25%).
Remember this? It's an oldie but a goody.
Speaking of periods closer to the modern era, yes, there were some Celtic incursions, and some Langobards ruled there. However, the problem arises that the yDna doesn not, to my knowledge, show large incursions. We know the Langobards were primarily U-106 and II. Those are not present in large quantities. There's a lot of R1b, mostly U-152. When the different subclades arrived is not yet clear, however.