The Reformers certainly identified the Roman Catholic Church as "Babylon the Great." They drew upon the symbolisms that seem to fit, at least, in their own minds. For example, John says that the "harlot" sits upon the seven headed beast each head representing "seven hills." Rome happened to be built upon seven hills. But, of course, if we take this literally, it would seem that the "beast" would represent Rome not the "harlot." And since it is the "beast" who destroys the "harlot", would this mean that Rome destroys the Roman Church?
The view of the Reformers was derived from the original understanding that "Babylon" referred to Rome (cf. Tertullian, Against Marcion, 13, and other writings of the early church fathers), and the Society's identification is of course a still later development from the Reformers' views (i.e. Rome -> Roman Papacy -> Christendom -> "world empire of false religion").
The seven hills indeed allude to the Septimontium of Rome, but there is much more to the image of Rome being built on seven hills. The author is explicitly alluding to the image of the goddess Roma, the patron and protectress of Rome (prefigured as the she-wolf who suckled Romulus and Remus), who was depicted on official coinage and in her temples as a woman seated on the seven hills. One coin dating to AD 78 was minted in Asia Minor which depicts both images of Roma (i.e. as a she-wolf and as a woman seated on the seven hills with a parazonium in her hand). This is a little detail that everyone who read Revelation in the late first century would have recognized but which is obscure today. The author very deftly subverts this sacred image of Rome by portraying the goddess as a gaudy whore.
I think you are confused about the matter of the Beast. The Beast represents not Rome but the "kings" who rule it (v. 10), i.e. the line of Caesars. And it refers specifically to an eighth king who is at the same time an earlier king (v. 11), and this king hates Rome and will destroy it (v. 16). This exactly corresponds to the Nero redivivus rumor that was widespread ... especially throughout Asia Minor ... in the late first century, as it was widely reported in both Greco-Roman and Jewish writings (cf. Dio Chrysostom, Oratio 21.10, Suetonius, Nero 57, Tacitus, Historia 1.78, 2.8, Dio Cassius, Roman History 63.9.3, 66.19.3, Sibylline Oracles 3.64-74, 4.119-124, 5.137-154, 361-374, 8.68-72, 12.78-94, Ascension of Isaiah 4:1-4, Commodian, Instr. 41.7), that Nero was not really dead or that he would come back from the dead (cf. Revelation 13:3), and that he would return with the Parthian army and destroy Rome. Nero was infamous for burning down a sizeable part of Rome, and the fear was that he would return to finish the job. He is described as a "matricide", the "fugitive from Rome will come, brandishing a great spear, having crossed the Euphrates with many myriads" (Sibylline Oracle 4.138-139). There were many pretenders who appeared in AD 69 and AD 80 and 88, claiming to be Nero (cf. Lucian, Adversus Ignorantum 20, who refers to a "false Nero" (pseudonerón), a term that recalls the "false Christs" (pseudokhristoi) of Matthew 24:24, Mark 13:22, Justin Martyr, Dialogue, 35). The supernatural origin of Nero redivivus, implicit in Revelation 13, is also found in Sibylline Oracle 3.63-74, Ascension of Isaiah 4:1-14, which identifies Nero with Belial (= Satan), and the number of the Beast in 13:18 corresponds to "Nero Caesar" in Greek gematria. Nero redivivus fills the antichrist role in earlier Jewish-Christian apocalypses, cf. Didache 16:4: "Then the deceiver of the world shall appear as the Son of God, and shall do signs and wonders (= Revelation 13:13-14), and the earth shall be delivered into his hands and he shall do unlawful things such as have never happened since the beginning of the world". In short, the Beast represents the Caesars of Rome, the last of which will be a king who had ruled sometime in the past (= Nero redivivus) and who would complete his destruction of Rome.