Slovenes are between one and a half million and two million people today. 100% ethnic Slovenes are even less. A very small population compared to Italians (Italy around 1000 AD had about 7 million inhabitants). When the Slovenes arrived in the Eastern Alps after the 6th century AD they were also a lot less. They also remained isolated from other Slavic migrations in the Balkans. Even if they wanted to, they could not have influenced Italians too much genetically.
How many were the Slovenes arrived between the 6th and 9th century AD? Between 20 thousand and 50 thousand? Not many more. I don't even think that Slovenes pushed all the natives out. Many were assimilated.
The Slovenes originally occupied much larger territory than today, though.
This map shows the original Slovene territory in the Early Middle Ages:
http://www.gis.si/egw/ZSS_T04_P02/index.html
http://www.gis.si/egw/ZSS_T04_P02/img/karta4.jpg
^^^
Actually I think that they extended more to the west also in Italy.
The peak of Slavic westward territorial expansion was in the 800s.
At that time the western boundary of areas with majority Slavic population was as follows: starting from the north-west, westernmost ethnically Slavic areas included: the Fehrman island, Wagrien region (Wagria) in what is today Holstein - including settlement Wendtorf in Kreis Plön (54°25′N 10°0′E) - then the outskirts of Hamburg, Lauenburg region, Lüneburger Heide, Wolfsburg region, Magdeburg region. South of Magdeburg the boundary of ethnic Slavic territory can be drawn as a meridional line extending up to Erfurt and the eastern part of the Thüringer Wald - in parts of Thuringia located to the west of the Saale River, the following area was ethnically Slavic during the 9th century: lands to the east of the line extending from the southern outskirts of Magdeburg, through the area of Erfurt, and up to the Thüringer Wald. From the Thüringer Wald the boundary was a line extending in south-western direction up to the River Main and the outskirts of Bamberg. From Bamberg the 9th century Slavic-Germanic ethnic boundary sharply turned towards Austrian Linz, and then once again turned meridionally, extending up to the Alpine city of Liezen at the River Enns.
In the Alps groups of Slavs migrated through mountain valleys up to East Tirol and the Upper Drava River. Slavs settled in north-western and south-eastern parts of East Tyrol, and in Italy they reached up to Julian Alps north-west of Udine and also settled in what is now the Provincia di Gorizia up to the coast of the Marano Lagoon. The city of Matrei in Osttirol (47°0′N 12°32′E) was called Windisch [= Slavic] Matrei as late as 1335.
First incursions of Slavs into Italy were reported already in the 590s.
Leszek Podhorodecki, "History of Ukraine", gives the following chronology for Slavic expansion:
"(...) At the turns of the 5th and the 6th centuries the Slavs, living until that time at the Dniester River, attacked the borders of the Byzantine Empire. The whole reign of Justin (518-527) and that of Justinian (527-557) were filled with combats against the Slavs pushing south across the Danube. They were especially active in period 545-557, because at that time they started to settle en masse in conquered territories [south of the Danube]. Only the incursion of the Avars into the Black Sea steppe and the lands along the Danube [years 561 - 569], hampered - for some time - the Slavic migration. After victorious wars against some of Slavic tribes, the Avars penetrated into the Pannonian Basin, and established their realm there. (...)"
The Avars showed up in the Pontic steppe around 560 and advanced westward to Pannonia along the northern bank of the Danube. Avar influence was not that unequivocally negative for Slavic settlement in the Balkans, though. Their initial attack against Slavs living north of the Danube (in Romania and southern Moldova) in the 560s drove some further Slavs - this time as refugees - south of the Danube, into the Balkans. Later there was a time when Avars were Byzantine allies against the Slavs (that was the case in years 584 - 585, for example), but in the end the Avars turned against the Byzantines and started to facilitate Slavic settlement. We can speak about two or three types of Slavic immigrants in the Balkans - those from tribes acting on their own, and those from tribes which accepted overlordship of the Avars, or signed alliances with them. The Avars also pushed Germanic tribes from Pannonia into Italy, when they defeated the Gepids (568) and forced the Langobards to emigrate (569). The disruption of the Gepids and the expulsion of the Langobards made a vacuum that West Slavs filled, migrating from Moravia into what is now Austria-Hungary-Slovenia.
Slavs were raiding Roman lands from their homeland north of the Danube river in what is now southern Romania since around the 490s, but they started to settle south of the Danube only since around 545. First settlements from ca. 545 - 550 were established in eastern Bosnia, Lower and Upper Moesia, and Little Scythia - including the regions of Ulmetum and Adina. Around the same time (ca. 550) first Slavic immigrants reached what is now Slovenia (they could be the same tribe which had besieged Durazzo in 547). Second wave of Slavs came to Slovenia after 568 (this time from the north, most probably from Moravia). According to John of Ephesus and Menander Protector another major wave of Slavs (Menander wrote that their strength was 100,000 but he didn't specify whether that included only warriors or all people) broke into Thrace and Thessaly as far as the Great Walls of Constantinople in period 577 - 580, and settled in vast areas. Sources mention that those Slavs were led by a war chief named Ardagast or Radogost (Ардагаст), and a king named Musokios. They could also reach as far as Greece "proper" already by ca. 580, when they sacked Athens, for which there is archaeological evidence (other sources indicate that Slavs started to settle in Attica and the Peloponnese only later, around 610).
In year 599 Pope Gregory I in a letter to Exarch of Italy wrote that Slavs had already seized most of Istria, and were penetrating (invading, raiding, etc.) into the Italian Peninsula. After mentioned invasions by Slavs, in 584 AD Byzantine Emperor Maurice sent emissaries to the Khagan of the Avars - Bayan I -, asking him for help against Slavs. The Avars initially worked as Byzantine allies against the Slavs. In 584 Ardagast with his 100,000 Slavs besieged Constantinople but was repulsed by combined Byzantine-Avar forces, and later lost two more battles against Byzantine-Avar forces led by Comentiolus (the battle of Erginia River and the battle of Ansinon, near Hadrianopole). Comentiolus also pushed Slavic settlers out of the region of Astica. In 585 the Byzantines and the Avars decided to attack the original Slavic lands across the Danube - forces under command of Priscus and Gentzon crossed the river at Dorostolon (Silistra) and surprise-attacked the Slavs in their native territory (as most of their forces had long been campaigning in the Balkans). They attacked at midnight and defeated the Slavs, but Ardagast eluded the attackers and escaped.
Later alliances switched - the Avars abandoned their Byzantine allies and instead started to cooperate with the Slavs, having subordinated some of their tribes (most notably one branch of the Dudlebes), and having signed alliances with other tribes.
Other early leaders of the Slavic tribes described by Byzantine, Italian and other sources - apart from Ardagast - include figures such as Musokios, Dabragezas, Usigard, Swarunas, Mezamir, Idarizos, Kelagastos, Chatzon, Waltunc, Kocel, Sandamir, Daurentios, etc.
These early names are often cited by linguists as a proof that Late Common Slavic was still one, mutually intelligible language at that time. 6th century Common Slavic was quite different from Slavic languages in later centuries. It preceded the ard-rad shift in Slavic.
For example at that time Slavs were still pronouncing [o] as short [a] - hence in modern Romanian language the word for grave is magura, and in modern Finnic languages the word for window is akkuna - both being loanwords from Late Common Slavic.
The word gard (town, stronghold) later changed into gord; then into grod in West Slavic*, grad in South Slavic, and gorod in East Slavic), the ard-rad shift had not yet taken place (hence there was Ardagast instead of the later form Radogost), etc.
*Except for Polabian and Pomeranian which retained the older gard form.
There were also Slavic pirates who raided the entire eastern coast of Italy, and even established some settlements along the coast. But I don't know what happened to those strongholds later (maybe they were driven out by anti-pirate expeditions or maybe assimilated).
"Historia Langobardorum" by Paul the Deacon describes Slavic raids into Italy and Langobard-Slavic wars.