As Christianity has branched into sects throughout history, have sects every agreed to recombine?

Seems like every point in christian history where there's a disagreement about context or translation, they split their church.

Well, no. That's a huge oversimplification. There have been plenty of disagreements that were resolved in other ways. Splits occur when one party (or both), say, "No, we're not happy with this solution and we're not going to tow the line, we're just going to go and do our own thing and you're wrong, not us."

What I really want to tackle as an erroneous assumption in your question is the basis of disagreements, and basis for reconciliations.

Has there every been a diplomatic or scientific process to settle disagreements? Would it be possible today, given the best academic, diplomatic and compromising setup we could come up with, to agree on one definitive version of the bible based on what we know of the language and all the earliest texts available?

The issue with framing the question like this is that most disputes are not about the text of the Bible. In fact, in terms of co-operation between different branches of Christianity, scholarly work on the text of biblical books is usually quite friendly, cordial, and agreeable. While different branches disagree about, for example, what books are in the Bible, disagreements about the original language texts are relatively minor. Even translation committees responsible for major translation projects into modern languages tend to be ecumenical and cross-denominational.

So, the barrier to unity among Christian churches is not located in language, texts, or versions of the Bible.

The main barrier, if I had to suggest one, is simply that church divisions generally stem from doctrinal differences - differences in what groups believe about God, about salvation, about Christ, about church matters. And these are hard to reconcile because those doctrinal differences form the constitutive elements of different groups.

/u/CChippy mentioned the unification of three denominations in Australia - Methodists, Presbyterians, and Congregationalists. A large majority grouping of churches of these denominations formed hte Uniting Church in 1977. Unsurprisingly, those local churches of the three denominations least likely to join the union, where churches theologically conservative and committed to their denominational tradition. Local churches most likely to join the union were those more theologically liberal - because doctrinal convictions by definition are not as important to liberal churches. Result? Doctrinal concerns are far less central to the Uniting Church than those other denominations, and it has consistently shifted in a theologically liberal direction.

Now, to be clear, I'm not intending to offer a judgment on the above, merely a historical observation.

Some groups have moved closer to reconciling splits. This has occured at the level of unification, as in the Australian example. The Eastern Catholic Churches are an example of a different sort - ancient churches of an Eastern type that popularly would be associated with Eastern Orthodoxy, but in fact have reconciled with Rome and been admitted to full communion in the Catholic Church while retaining their distinct traditions (not all ECCs follow this pattern, e.g. Maronites, but it is true for the majority). Some churches move towards recognition of each other, without dissolving into a union.

So, there are diplomatic efforts under the umbrella of ecumenism, but the location of the causes of schism are not easy to 'fix', and your question about language/texts/academic/scientific process mislocates the 'problem' of unity.