I feel that the objectives of the US are not set in stone in total, but they are hard to change. We should never overlook the fortunes of random chance, regardless of how likely they are. I refer you to the Marquesas example - if the US forces never lost control of the islands, then they would have kept de facto possession through the end of the war, and de jure protectorate later on. This would lead to American presence in Polynesia nearly a century ahead of the OTL schedule, which will do quite a bit to change the mindset of the American public. It is on the bottom end of the priority list, but it gets added to the list. One could say the same thing about Liberia if it somehow became an official government project - if the US has a small presence in Africa in 1820, by the 1870s, the US would have maintained that presence for 50 years, leading it to be a traditional region of interest, and it'd be added to the (bottom) of the list, which could make further expansion proceed in the region viable.
Or, instead, look at the Mexican-American war: The US provided the negotiator a certain amount of money (12 million, I think? been a while) to purchase all of Texas's claims, New Mexico, and Alta & Baja California, while appropriating a smaller amount (6 million) for additional gains afterwards. OTL, the US Negotiator, Trist, was opposed to major expansionism and didn't even go for the minimum amount in his instructions, and he couldn't be replaced as Polk wanted this done under his term. But if a more expansionist US negotiator, combined with a poorer Mexican one, could easily lead to more land being ceded. Parts of Sonora/Chihuahua, and maybe even more. It's similar to how the US originally only desired Luzon, but bumbled its way into a victory that lead to them taking the entire island chain. fortuitous circumstances can put to rest even the best-laid plans.
Cuba, I feel, is between 1 & 2 on my list, as it was considered vital for the defense of the Heartland, as its possession would protect the routes to New Orleans and the Mississippi. Combine that with the Yucatan, and you have US possession of all land bordering the channels leading to the Gulf of Mexico, and you've made it, practically, an American lake. I would not understate the value of that. Digressing, Cuba would be annexed pretty early on, as it did have a very large European population and if it did join, it'd be the most easily integrated possession in the area. You're correct on the anti-Catholic bias, but considering the cost/benefit of integrating the island, it would be the one state that could most easily overcome that concern.
Many of these proposed annexations are longshot (looking especially at you, Albania. So long a shot it doesn't fit on the screen), and do not fit well into OTL priorties for the US. However, they are great to have compiled into a single list to show all that were even considered by adventurers (whether or not they actually had a chance to succeed). And, for most of these, a timeline could emerge where securing one of the listed possessions might actually fit into US territorial interest.
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I'd also point out that, just as the US was starting to fill out its continental boundaries and begin to look overseas, they suffered from the Civil War and, as a result, lost more men as a percentage than the British did in WW1. They were devastated by the war and had to take time to recover, hence the US drawing into itself for a few decades. Avert the massive casualties, and you could (important word, not would) find a world where the US is much more assertive in the 1860s-1880s. That alone would alter the fabric of the country's conscious as well, so the results would be immense, either way.