Do not be convinced of things until they are tested and proven. It is not prudent to be convinced of things before doing so. Propose something, and test it to see if it fits. "Test all things, and hold on to the good". If it is good, more people (at least those who reason) will be persuaded.

Sure. As the in-house skeptic, I'll politely and humbly help check interpretations and keep people honest, and ask questions that should be asked. "As iron sharpens iron, one man sharpens another". Good questions will result in good interpretations. I'm also keeping an eye on Trump, in case I'm wrong.

I'm pretty sure Daniel 7 actually says "kingdoms," not kings.

There's no need to be pretty sure when you can be sure; this is straightforward to check online or in a paper Bible. These things are important enough to check for accuracy before proceeding. Daniel 7:17-18 uses both the term 'king' and 'kingdom'. The beasts are said to be kings.

Daniel 7:17-18

‘These four great beasts are four kings who shall arise out of the earth. ¹⁸ But the saints of the Most High shall receive the kingdom and possess the kingdom forever, forever and ever.’
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... because the span of a kingdom is (or was, I should say) defined by the lifetime of its ruler. When King Nebuchadnezzar died, for example, it could be said that his 'kingdom' was over.

No, that's not how the usage suggests its interpretation. 'King' can also mean the office or the title, not just the specific person. For example, in Exodus, a sequence of men held the office of Pharaoh, but the Bible never differentiates them by name. They are all just referred to as "Pharaoh", from the one who ordered the killing of the Israelite babies, to the one Moses contended with during the Exodus 40+ years later. When a king dies, his kingdom is not over; his reign is over. We can tell from Daniel 7 that the kingdoms do not end with the death of a king because it says this:

Daniel 7:11-12

¹¹ “I looked then because of the sound of the great words that the horn was speaking. And as I looked, the beast was killed, and its body destroyed and given over to be burned with fire. ¹² As for the rest of the beasts, their dominion was taken away, but their lives were prolonged for a season and a time.
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The rest of the beasts existed through all of the rise and fall of the Little Horn, etc. and are then permitted to continue to exist for a while though their dominion is taken away. If we reconcile this with Revelation 17 and 13, the idea that these are individual persons doesn't work. It looks like the cultures that these beast represent will continue to exist, though their political power will be taken away when the Kingdom of God is established.

There are two fulfillments of these signs. One is the traditional sequence of

• Babylon,

• Persia,

• the Greeks, (Alexander, and his four generals who split up his empire)

• Rome,

whose horns give rise to the kingdoms of western Europe, of which the Papacy is the Little Horn. (This was what was taught for centuries; all of the notable Protestant theologians from the Reformation up until the end of the 1800's taught that the Papacy is the Antichrist. See the observations on Historicist eschatology.)

The second, which seems uncanny to me for how well it fits, appears to fulfill the part about their dominion being taken away while the cultures remain after the establishment of the Kingdom of God:

• The lion with eagle's wings which were broken off and stood up and became like a man, and the mind of a man was given to it— That would be Britain, and the United States. Britain's symbolic animal is the lion, and the United State's symbolic animal is the eagle. The United States broke off from Britain. Whether you take it that the lion or the eagle's wings stood up and became like a man, both work: the modern world's developments, from physics to medical science to economic institutions like modern banking and corporations, to the form of constitutional democracy and even constitutional democratic monarchy all over the world came from the US and Britain and it's intellectual developments. To a stunning extent, "the mind of a man" seems to explain the intellectual output of the US and/or the UK.

• The bear with three ribs in its mouth, reared up on one side—That would be Russia. Russia is recognizably symbolically identified with the Bear, and the "mouth" of Russia, where it interfaces navigable European waters, has three thin Scandinavian nations sticking out of it—Norway, Sweden, and Finland. I do not know what exactly it means that it is reared up on one side, but Russia is definitely lopsided in its distribution. All the wealth and power and development is concentrated on the European side, and the rest is sparsely uninhabited.

• The leopard with four heads and four wings of a fowl on its back, and dominion was given to it: This represents Germany and France, and the times they came together whether in cooperation or conquest (such as the Holy Roman Empire, the European Union, Napoleon's conquest of Germany, Hitler's conquest of France). Germany as we know it today arose out of Prussia unifying the other Germanic states into one nation, and Prussia was symbolized by a leopard. (Old World War I posters and political cartoons showing the leopard with the spiked helmet, for example.) France is symbolized by a rooster in political cartoons, even to this day. I admit this part is a bit messy, but Germany has gone through four "reichs", with the current dominion of Germany over European economics appears to be the fourth. Or the fourth might be a future reich.

The fourth beast's original fulfillment was Rome, and the little horn was the Papacy, and in modern times, the second fulfillment has it that the fourth beast will be when ten kings come to power and give their power and authority to the Papacy (according to my interpretation).

"As for the rest of the beasts, their dominion was taken away, but their lives were prolonged for a season and a time" seems to me to say that Britain, the US, Russia, Germany, and France will all continue to exist for a while after the Kingdom of God is established, but their dominion is taken away.