One future restaurant owner who emigrated from Italy to the U.S. in the 1920s described his early impression of Italian food in the US: it was "just for fun called Italian. As a matter of fact, I found [spaghetti with meatballs and cotoletta parmigiana] extremely satisfying, and I think someone in Italy should invent them for the Italians over there."

Italian food in the U.S., then, isn't a facsimile of any one local or regional Italy-Italian set of dishes. It draws from a lot of different places, but through an American filter of--as OP guessed--much better access to meat, preference for less garlic, and immigrants often from northern Italy running the restaurants that served a largely southern Italian-American clientele.

When Italians immigrated to the US en masse in the early 20th century, they tended to settle near other ex-Italians--hence all the cities with a Little Italy or its equivalent, or some individual towns as a whole. For a few reasons, food rather quickly became a very community-forming/bonding nexus. As Hasia Diner (really, that's her name) found, letters from Italian immigrants back to Italy stress again and again how overwhelmed and thrilled they are with the abundance of food in America. They talk extravagantly of all the meat they eat and all the wine they drink. A 1910s version of curating your life on Twitter? Trying to get your relatives to immigrate? Probably, but the repeated theme suggests at least some underlying reality.

In cities, lack of access to farmland meant people cultivated rooftop and other common spaces as gardens--community gardens, another nexus of identity as Italian-Americans. Massive family dinners or church parties became sort of an "in your face" to discrimination. And home ec teachers despaired over their Italian students whose mothers were teaching them to cook at home. (Among other things, diet science in the early 20th century held that eating spicy food led to sexual profligacy.)

So with food as general bonding site for communities composed of Italian-Americans with ancestors from different regions, there was already a mixing of local traditions. Restaurants, though, played a large role in the development of the Italian food that was Italian "just for fun," and did often have a northern spin.

19th century America had already hosted a number of restaurant owners and chefs with a northern Italian background. Their menus generally focused on French or similar cuisine trends at the time--but still with some modified versions of Italian dishes. And when Italian migrants started arriving in the early 20th century, they found good work as waiters or line cooks in the restaurants owned by people with more-often northern Italian heritage.

So then in the 1930s, of course, less-poor Italian-Americans with a restaurant employee background started founding their own restaurants, not just proto-food trucks (food wagons and other street vendors). And they brought an Italian American food background, selection, knowledge--and community identity.