Do any principles commonly used in the field of hermeneutics have any counterparts in scientific principles? Is there a corollary in hermeneutics to the requirements that science demands as far as the reproducibility of experiments, peer review of results, etc?
There have been theologians historically who tried to use a scientific method of theology (and so presumably of hermeneutics)—specifically the Old Princetonians (Archibald Alexander, the Hodges, Warfield, etc.). Also, higher criticism, Hegelian and Kantian theology all have tried to apply their various views of science to theology and textual interpretation. There's a sense in which scholastic theologians such as Aquinas also took a scientific approach. Sorry that this answer is in such general terms.
Of course, all good hermeneutics will share some basic tools in common with science—logic, etc. However, there are fundamental differences between the two which make it dangerous to apply the same principles.
Science deals primarily with historic revelation; in making the world, God reveals himself. Biblical hermeneutics deals with historic revelation which is administered in the present. Thus the living, active nature of the Word of God; it is a historic revelation which is given to the individual united to Jesus Christ in a special way in the present. Thus, science is more active, and hermeneutics is more passive. Also, science has as its end information, structured models; theory is its goal. Biblical hermeneutics has personal knowledge as its end and not a conceptual model. For this reason, to apply too many scientific techniques can be stifling to the relational aspect of interpreting the Scriptures.
Because of the rules of sensus plenior, the meaning is reproducible and verifiable. It exists like a giant crossword puzzle, but rather than words crossing and tying the solution, whole passages, cross, metaphoric meaning is locked, and theology is consistent with the literal Bible.
Consider a cipher where words are replaced with metaphoric meanings. Garments are always works, donkeys are always prophets, blood is always life, water is always the word, light is always holiness in it's various aspects, and darkness is always grace. Replace those few words everywhere they exist in scripture then find a sensible, theologically sound double entendre wherever they occur. It is humanly impossible to construct such a cipher, yet that is what the rules of sensus plenior demand. Nothing short of divine authorship is acceptable.
Likewise, since all nature testifies of Christ, there are legitimate metaphors in nature. But since they are not revealed prepositionally as in the scripture, they are more difficult to discern. But we have a "more sure word of prophecy" in the scriptures.
The tolah worm is an example.
Physics might be better suited with a model taken from Genesis 1. Since there is nothing larger than God, when he created the void, he created it within himself. We are the voids within God. He made room for us. Now view the physical model of reality where what we think of as primary particles are discontinuities within a hyper-dense plenum. Gravity is caused by the plenum moving to it's lowest energy state and pushing the discontinuities together. Charge is a discontinuity that placed the plenum in tension or compression. Opposite charges move together to reduce the stress. Magnetism is a discontinuity with tension at one end and compression at the other. Energy and mass interchange as the localized energy creates a discontinuity, or a discontinuity collapses and throws energy back into the plenum. Hyper jumps occur when particles of the plenum are lined up and move simultaneously permitting the void to jump without existing between the points of travel. When an electron enters a nucleus, the nucleus void becomes unstable and spits out another electron void in another direction as it collapses to a stable configuration.
In this model, since all the properties belong to the plenum and the geometry of the voids, you automatically have a unified theory.