Josh, I don't think that at this time you could come up with a better or more relevant question.
Most Christians who take any interest in prophecy are looking to Israel and the middle east for all the signs and fulfilments of prophecy. They think that while the USA may be having an indirect impact on prophecy through its support of Israel, they don't recognise any direct prophetic relevancy or role for the USA in the Bible prophetic scenario for the end times. But you are correct in pointing out that the SDA church has a very different perspective, and is quite unique amongst those who study prophecy for the last days. I can see this thread diverting into all sorts of directions, with every Tom,Dick, and Harry offering their personal or church's view and give the SDA perspective little attention because it grates on many nerves and is too close to home. Yet our eschatological view hasn't changed in 160 years. In the beginning, it was considered extremely unlikely because of the political and religious mood in the 1880s, but today, things have dramatically changed, and the SDA picture as we see it is becoming very quickly the only likely scenario.
So here is a very brief summary of what has been our belief for well over a century. And has not changed.
In the 19th century, Catholics were only admitted into the US on sufferance. The pioneers of the US had no liking for the papacy, having all escaped a tyrannical Europe. They saw the papacy as a dangerous enemy. But they had just written a bill of rights and signed off on religious and political freedom. Therefore everyone was welcome, despite the fears many held, particularly of the Jesuits.
SDA teaching has it that the sea beast of revelation 13 is the papal power. A composite of all the powers that preceded her... Babylon, Media-Persia, Greece, and pagan Rome. Many attributes and characteristics of those former empires can be seen in the Catholic system. They have been discussed numerous times elsewhere, so no need to elaborate here. That beast was to receive a mortal wound which would be healed. It would also rule for 1260 years, following the day for a year formula established previously in prophecy in Numbers and Ezekiel, and born out in many fulfilments, most notably the messianic prophecy of Daniel 9. The papacy's first tenure at the top began in 538, and concluded in 1798. In 1798 it's power as a civil ruler was broken. Many European nations thought at that time the Catholic church finished. She was temporarily finished as a union of church and state, but she continued in her role as a religious entity.
At this time, in the late 18th and early 19th centuries, the second land beast of revelation 13 began its rise to power. This new kid on the block would rise to such prominence that she would restore the prestige and power of the first beast, but on a global scale, giving the Vatican unprecedented control over the nations and over the world religious framework. All this is taking place right now, through the ecumenical work, particularly of the late pope Francis, and looks to be continued by the new pope Leo. It is no coincidence we believe, that the new pope is American, and is following in the footsteps of former Leo's, and has already spoken strongly in favour of ecumenism. We believe, and not without a great deal of biblical and historical evidence, that that seconds beast is the USA, and will, through forming an image to the first beast, a union of church and state, usher in a new era of papal tyranny on a global scale.