So I think there's a lot to unpack in your question. While the very clear growth of Atlantic trade after 1492 relative to the saturated Mediterranean trade certainly benefited Atlantic-facing regions much more than Europe's pre-modern economic powers, it's a bit daft to attribute Italy and Greece's current economic issues to any of that over more recent, and modern, economic events; most of which fall within our twenty year rule (especially because other European economies that have stagnated in the past decade, like Spain and Portugal, are Atlantic-facing). And in any case, according to Eurostat, Italy is the third-largest economy in the Eurozone, while Greece is very close to Europe's median (you can see that data here). Both the Italian and Greek economies are beset by stark inequalities spanning different professional categories and regions, but both are high-development OECD countries with per-capita income levels comparable to their neighbors. While many European countries are, like most advanced economies, dealing with the consequences of post-industrial society, your statements about the United Kingdom being the only economically significant Atlantic-facing nation in Europe is flatly incorrect, Germany has a larger economy than the UK while France isn't far behind (you can see the full list here, although this might be the rare case where Wikipedia has the data displayed better.

And while Atlantic trade certainly was important, it doesn't even tell the whole story regarding pre-industrial development: Northern Italy remained amongst Europe's top three highest GDP-per capita regions until around 1820 (according to Angus Maddison's research on historic GDP levels). Indeed it is not a consequence of happenstance that the center of the Roman Empire was a peninsula characterized by dense urbanization, high agricultural productivity, and central position in the shallow Mediterranean Sea. Political fragmentation and instability after the end of the Empire, then, was not really a cause of economic stagnation, but rather made possible by economic prosperity (I wrote about how that impacted Medieval Italian politics a few months ago, in this answer. Clergymen, judges, and lawmakers seated in Italian cities would continue to be elected, in the Roman fashion, by colleges of prominent citizens, and these cities retained legal systems based on Roman-era freedoms and enfranchisement, with impersonal codified justice and protection of property rights, not just land rights. This was all capped off by the Mediterranean trade, which created extensive networks exchanging goods and services operated by a large middle class, which wasn't willing to be taxed without a say in the matter, creating inclusive institutions. And this isn't a wholly Italian phenomenon: other politically fragmented and heavily urbanized areas, like the Netherlands, developed a similar set of laws and institutions. In fact, the Netherlands come in a close second to Italy in economic development indices through the middle ages up until the early modern era, when the double whammy of the Italian Wars and the boom in atlantic trade sent the Netherlands on a trajectory surpassing the Italy.

Italy would only really begin lagging behind the rest of Europe after the Industrial Revolution. Take Britain, the example par excellence of industrialization (and, later, industrial decline): prior to the industrial revolution, the British Isles were sparsely populated and (or because they were) agriculturally unproductive. In an epoch where travel was difficult, to say the least, a low population made for scarce labor; meaning laborers England could command wages that were relatively higher than those of their counterparts in the rest of Europe, not only allowing for a higher standard of living in spite of the smaller economy, but also incentivized employers to make these expensive workers as productive as possible. Further, poor terrain also makes for an landowning aristocracy that is not much wealthier than the mercantile middle class (at least when compared to places like Italy, as well as other places like parts of France) hence allowing the middle class to push for strong political enfranchisement, in turn creating a legal and political system favoring investment and entrepreneurship.

Italy, on the other hand, was incredibly agriculturally productive, and the agricultural productivity increased as you moved south: just think that the ancient Romans believed that the goddess of agriculture, Ceres, lived in Sicily. But Northern Italy too is perfect for the growth of rice and grain. This had a measurable impact on Italian economic development; Italian entrepreneurs saw no reason to industrialize well into the 19th century (in addition to allowing the peninsula to sustain the existence of many fragmented independent states for numerous centuries). Indeed, nearly all scholarship on Southern Italian economic development agrees that the capitalist class in the Kingdom of the Two Sicilies, in the south, was heavily biased towards acquiring more extensive agricultural possessions, rather than rendering their existing possessions more efficient and lucrative, and were totally disinterested finding other enterprises to invest in; there just wasn't any point.

But, and you must forgive me for repeating myself here, that isn't the whole story. In Italy there is enormous variation in historic industrialization levels (I explain the reasons for that in this, admittedly long, answer); in the North, where there was the most political fragmentation, institutions did a lot to foster economic development, and even, albeit in some places more than other, helped industrialization along (you can read more about that in this answer, although there's a lot of overlap with the answer linked above). You might also be interested in this other answer about the Italian economic boom in the 1960s.

I haven't written much about Greece, you'll notice; I can't say I know as much about Greece than I do about Italy. But do keep in mind that Greece is a much smaller country than most think; with only eleven million inhabitants, and serious industrialization requires large economies of scale for both production and consumption that the Greek economy, until recently, did not have access to. Greece peaked early, so to speak, but didn't have the conditions to progress beyond a certain level; and Greek entrepreneurs certainly could have benefitted from a large market when part of the larger Ottoman Empire (institutional conditions permitting, which they weren't) but right when industrialization was developing Greece began its conflict for independence.

A source you might be interested in is V. Zamagni's "The Economic History of Italy, 1860-1990" (OUP, 1993) and for a more general overview on Italian history John A. Davis' "Italy in the Nineteenth Century, 1796-1900." English-language literature on Italian economic history is sorely lacking however, but if you can get your hands on the following paper through perhaps a university library database, you could read “The ripples of the industrial revolution: exports, economic growth, and regional integration in Italy in the early nineteenth century”, in the European Review of Economic History (2014).