I think the answer lies in a theological disposition. There are two significant things that explain to me how the hermeneutic works. First Darby and the Plymouth Brethren had the "notion of a clergyman was a sin against the Holy Spirit, because it limited the recognition that the Holy Spirit could speak through any member of the Church." This is one of the significant dispositions.
The second disposition can be found outside of dispensationalism. Before Darby's generation many theologians experiencing the revivals under George Whitfield, Jonathan Edwards, etc.,were taking a sort of futuristic view of many parts of Revelation. The revivals themselves seemed almost like a new 'dispensation'. The idea of a 'rapture' was not formed yet but pretty close.
For example in Jonathan Edward’s History of Redemption:
Then an end is brought to the Jewish commomvealth in the destruction of their city and country. After that, an end is brought to the old Heathen empire in Constantino's time. The next step is the finishing of Satan's visible kingdom in the world, upon the fall of Antichrist, and the calling of the Jews. And last will come the destruction of the outward frame of the world itself, at the conclusion of the day of judgment. Heaven and earth began to shake, in order to a dissolution, according to the prophecy of Haggai. (P323)
Now I have these two dispositions, one leading up to Darby and one within Darby himself. From here, as someone who was momentarily a dispensationalist in the first year of being a Christian, I think I know the hermeneutic. First the emphasis on the Holy Spirit, and rejection of most tradition, traditional churches are viewed as more or less dead. Dead meaning not filled with the Spirit. Secondly taking lead from the previous generation who were lively and excited about future prophecy, Antichrist, salvation of Israel, etc. a unique suspicion arose.
The suspicion is this: Those dead churches are always quenching the Spirit by their traditions, and one way in which they remain cold and lifeless is to take everything in the Bible as a metaphor. They avoid the literal requirements of the Bible in order to maintain their carnal lives. Therefore, in the same way they have been removing the power of the book of Revelation. They do not have faith to take it literally, so everything is a symbol.
So the hermeneutic is partly subconscious and it simply says committed Christians need to take the Bible as 'literally as possible' and if that means imagining 1000 year reign of Christ as physical, then so be it. But when no logical meaning can be obtained from a metaphor, no matter how imaginative, then it has to be a metaphor. This is almost seen as a last resort, for literal views are the first goal, given the frustrated or excited emotional state and distrust of lukewarm clergy.
We tend to look at these extreme conclusion as ridiculous, at least I do on some points like the 1000 years, but I party understand how a person can be driven to that extreme. I can also see why a person feels the need to become extreme, when so many seem very cold and lifeless. I think my answer explains why dispensationalism appeals more to nondenominational Bible churches, Baptists, Pentecostal and Charismatic groups. Having said all this, I do not look down on those churches at all. God loves all those brothers and sisters in Christ and so should we.
When looking at dispensationalism we must not focus on the idea of dispensations, but of a future one in Revelation. This future dispensation is linked with Israel which also provides a new view of some parts of the the Old Testament, not shared by those who do not fully buy in to the movement. However, the basic idea of the two main 'dispensations', that of Law, versus that of Grace, was not at all new to Darby. Today under the lens of Biblical Theology, which emphasizes the unity of both covenants, we sometimes forget many of the reformers often also stressed the differences of these covenants. Biblical Theology, though very useful, is not the be-and-end-all for many Evangelicals. Many of us are a hybrid of different labels.
Luther especially stressed the two 'dispensations' while not being a 'dispensationalist':
We will not have Moses as ruler or lawgiver any longer. Indeed God himself will not have it either. Moses was an intermediary solely for the Jewish people. It was to them that he gave the law. We must therefore silence the mouths of those factious spirits who say, “Thus says Moses,” etc. Here you simply reply: Moses has nothing to do with us. If I were to accept Moses in one commandment, I would have to accept the entire Moses. Thus the consequence would be that if I accept Moses as master, then I must have myself circumcised,4 wash my clothes in the Jewish way, eat and drink and dress thus and so, and observe all that stuff. So, then, we will neither observe nor accept Moses. Moses is dead. His rule ended when Christ came. He is of no further service. (Luther's Works Volume 35.164)
Again one can prove it from the third commandment that Moses does not pertain to Gentiles and Christians. For Paul [Col. 2:16] and the New Testament [Matt. 12:1–12; John 5:16; 7:22–23; 9:14–16] abolish the sabbath, to show us that the sabbath was given to the Jews alone, for whom it is a stern commandment. The prophets referred to it too, that the sabbath of the Jews would be abolished. For Isaiah says in the last chapter, “When the Savior comes, then such will be the time, one sabbath after the other, one month after the other,” etc.6 This is as though he were trying to say, “It will be the sabbath every day, and the people will be such that they make no distinction between days. For in the New Testament the sabbath is annihilated as regards the crude external observance, for every day is a holy day,” etc. (Luther's Works Volume 35.164)
Even the Westminster Confession of Faith noted various or "manifold dispensations" in 1646 article, here.
So really the theological disposition at work is simply an excited desire to make a literal view of everything in the Bible to create a future predicted 'dispensation'. The two main dispensations of Law and Grace are borrowed from many of the reformers and puritans.