The big difference between the Balkans (including Greece) and Italy is that they experienced the Slavic migrations or invasions as you prefer. We did not, and even the Lombard invasions were limited in scope. Even in the Balkans the "Slavic" influence was not as great as the politics of the Pan-Slavic movement would have you believe. I have no personal stake in the matter. It's just that facts are facts, no matter how inconvenient they might turn out to be.
Thank you for admitting that the Slavic migration actually occurred and had a visible genetic effect, even on Greeks. You can bet how much it had on others. I also agree that the Pan-Slavic ideology changed the later perception of the ethnicities on Balkan peninsula, but the main "victim" of that ethnic "mascherade" were people called Croats, not ancient Roman Dalmatians if it was you thought. I can further elaborate that.
As for your conjectures about the Roman Empire, take it up with Ralph and Coop, who find no major input into Italy after about 400 BC except from the Balkans, or at least they see exchange after that period between the Balkans and Italy. If ancient dna proves them wrong, fine with me. If you're going to take over most of the known world you're going to absorb some of those peoples; if you're stuck in some out of the way, climate challenged place, not.
Ralph and Coop is my favourite paper! Thank you for mentioning it because I was up to do it anyway. Have you seen the image:
https://doi.org/10.1371/journal.pbio.1001555.g005
It is called: "Estimated average total numbers of genetic common ancestors shared per pair of individuals in various pairs of populations, in roughly the time periods 0–500 ya, 500–1,500 ya, 1,500–2,500 ya, and 2,500–4,300 ya."
If one takes a look into the 3rd row (1,500–2,500 ya which is roughly a Roman Period) and 1st column (S-C, which means West-South Slavs), she may notice that S-C share almost the same number of ancestors within each other as they do with PL (Poles). At the same time the shared ancestry with all others, including Italians (IT), is insignificant.
Then if one looks at the later time period 500–1,500 ya (the chart above) which is the time when the great migration has started including the whole medieval period, she can see a significant drop of the ancestry that West South-Slavs share with Poles, where the shared ancestry among them is still high. At the same time the shared ancestry with combined Romanian-Bulgarian group gets its peak.
Then there is the last chart on the top, a period 0–500 ya, where the shared ancestry with Poles is practically absent as well as with the Romanians/Bugarians.
Ralph and Coop told us through genetics such a wonderful migration story of West-South-Slavs from the land where they lived together with Poles, but that land was not "Balkan" nor a Roman Empire. And we have historical records of that migration.