Has the Church historically considered biblical texts concerning slavery to be transcultural or finite? How have the Bible's passages concerning slavery been interpreted and applied throughout Christian history, especially passages such as Exodus 21:2-11, Leviticus 25:44-46, and 1 Timothy 6:1-2?

Have Christians historically applied these passages to employer/employee relations as many commentators have suggested, or is this an inappropriate cultural parallel?

Note that I am not asking, "Does the Bible condone slavery?" You may of course share your opinion on this question when giving your response (I understand that this question is somewhat implicit), but I am specifically interested in how the Christian Church has historically interpreted and applied these passages.
Historically, these verses have not been applied to employer/employee relations, at least not in the sense that we understand employment today.
In ancient times slavery was fairly common; employment, however, was not. Most free people lived and worked on the family farm. Employment contracts did exist, but only to protect the employer's interests. Contracts usually bound the employee to the employer for a set time; as such, employment was just a limited form of slavery.
In medieval times slavery was gradually replaced by serfdom. Serfs had more rights than slaves but were bound to the land on which they worked. If the land was sold the serfs were required to work for the new landowner. Employment remained a subset of slavery.
With the rise of the merchant class and the beginning of the industrial revolution this began to change; however, as recently as the early 1900s the majority of the population even in industrialized nations lived on family farms. Instructions on employer/employee relations simply were not relevant to most people's lives.
With all that in mind, it should not be surprising that commentators historically have not applied these texts to contractual employment.

Here's a few examples of what they have said.
In the 4th century, John Chrysostom wrote commentaries covering most of the New Testament. He did not comment on 1 Timothy 6:1-2, but he did say this about Colossians 3:22.

“Servants,” he saith, “obey in all things your masters according to the flesh.”
And see how always he sets down the names, “wives, children, servants,” being at once a just claim upon their obedience. But that none might be pained, he added, “to your masters according to the flesh.” Thy better part, the soul, is free, he saith; thy service is for a season. It therefore do thou subject, that thy service be no more of constraint. “Not with eye-service, as men-pleasers.” Make, he saith, thy service which is by the law, to be from the fear of Christ.

Commenting on 1 Corinthians 7:20-21, Chrysostom said,

“Let each man abide in that calling wherein he was called. Hast thou been called, having an unbelieving wife?  Continue to have her. Cast not out thy wife for the faith’s sake. Hast thou been called, being a slave? Care not for it. Continue to be a slave. Hast thou been called, being in uncircumcision? Remain uncircumcised. Being circumcised, didst thou become a believer? Continue circumcised. For this is the meaning of, “As God hath distributed unto each man.” For these are no hindrances to piety. Thou art called, being a slave; another, with an unbelieving wife; another, being circumcised.
Astonishing! where has he put slavery? As circumcision profits not: and uncircumcision does no harm; so neither doth slavery, nor yet liberty. And that he might point out this with surpassing clearness, he says, “But even (Αλλ' εὶ καὶ δυνάσαι) if thou canst become free, use it rather:” that is, rather continue a slave. Now upon what possible ground does he tell the person who might be set free to remain a slave?  He means to point out that slavery is no harm but rather an advantage.

Jerome, writing Against Jovinianus, referenced Exodus 21. He said the laws about setting slaves free do have application outside the physical practice of slavery, but he was thinking in terms much larger than employment contracts.

And if we read that every Hebrew keeps the same Passover, and that in the seventh year every prisoner is set free, and that at Jubilee, that is the fiftieth year, every possession returns to its owner, all this refers not to the present, but to the future; for being in bondage during the six days of this world, on the seventh day, the true and eternal Sabbath, we shall be free, at any rate if we wish to be free while still in bondage in the world. If, however, we do not desire it, our ear will be bored in token of our disobedience, and together with our wives and children, whom we preferred to liberty, that is, with the flesh and its works, we shall be in perpetual slavery.

In early modern times, Bible commentators focused on the plain meaning of the text or extrapolated to general moral principles.
Matthew Henry comments on Exodus 21

The Israelites had lately been servants themselves; and now that they had become, not only their own masters, but masters of servants too, lest they should abuse their servants, as they themselves had been abused and ruled with rigour by the Egyptian task-masters, provision was made by these laws for the mild and gentle usage of servants.

He adds, a little later,

This law will be further useful to us, (1.) To illustrate the right God has to the children of believing parents, as such, and the place they have in his church. They are by baptism enrolled among his servants, because they are born in his house, for they are therefore born unto him, Eze. 16:20 . [Emphasis in original]

Henry extrapolates a further application not to employees but to children, because like servants they belong to the household.
John Gill says

Now as this servant, in the state of servitude, was an emblem of that state of bondage to sin, Satan, and the law, which man is brought into by his theft, his robbing God of his glory by the transgression of his precepts; so likewise, in his being made free, he was an emblem of that liberty wherewith Christ, the Son of God, makes his people free from the said bondage, and who are free indeed, and made so freely without money, and without price, of pure free grace, without any merit or desert of theirs; and which freedom is attended with many bountiful and liberal blessings of grace.

Regarding 1 Timothy 6, Henry says,

Here is the duty of servants. The apostle had spoken before of church-relations, here of our family-relations. Servants are here said to be under the yoke, which denotes both subjection and labour; they are yoked to work, not to be idle. If Christianity finds servants under the yoke, it continues them under it; for the gospel does not cancel the obligations any lie under either by the law of nature or by mutual consent.

John Wesley says,

6:1 Let servants under the yoke - Of heathen masters. Account them worthy of all honour - All the honour due from a servant to a master.Lest the name of God and his doctrine be blasphemed - As it surely will, if they do otherwise.
6:2 Let them not despise them - Pay them the less honour or obedience. Because they are brethren - And in that respect on a level with them. They that live in a religious community know the danger of this; and that greater grace is requisite to bear with the faults of a brother, than of an infidel, or man of the world. But rather do them service - Serve them so much the more diligently. Because they are joint partakers of the great benefit - Salvation. These things - Paul, the aged, gives young Timotheus a charge to dwell upon practical holiness.

Gill says,

these things teach and exhort;
the Syriac and Arabic versions add them; the servants. The apostle was not above instructing and exhorting persons of such a capacity, and in so low a state of life; and it became Timothy to do so likewise; and every minister of the word.

None of these commentators gives the slightest hint that they thought this passage could apply to employer/employee relations.