This is a fantastic post and I hope there are more like it! I am very tired of talking about literal interpretations of sacred texts and this is very refreshing. I will try to respond to a few of your questions below. I should note that the sacred texts are not really a part of my own spirituality but I do enjoy studying them.

I am curious as to what authority are you appealing to when you claim that this is okay to do.

I think it is always 'okay' to interpret, or "read into" texts. I actually think it's impossible not to. That's why we teach our students about literature. Even literal interpretations are interpretations. Different people have read passages differently over time. So your question might be: How can we do this without becoming relativists about their meaning?

Briefly, there are several ways of studying a text, such as asking (1) What was the intended audience? (2) Who was the author, why was he writing? (3) What was the historical context? (4) What is the genre? (e.g. Genesis might be poetic and mythical, but Leviticus looks more like a code for a particular set of people in history). In this sense, the interpretation is not subjective, but based upon historical and literary inquiry. It's true that there is a personal and subjective component to reading sacred texts, but this has more to do with its application to your life and its meaning.

Speaking of meaning...

If the text was divinely inspired, you must grant that the text does exactly what it was intended to do.

This has to do with how we view "truth." Truth is still being communicated despite hugely different interpretations, how could that possibly be? We can go further on this, but I think it's important to note that Christians view their texts as "inspired" not "communicated verbatim," so Islam has the up hill battle hear. Christianity accepts that their authors had their own purposes but also had a divine purpose as well.

So can the meaning of a text change? Certainly its significance can. Christians have a very sweeping and global view of their text. The way we read the Bible may affect the course of history differently at different times. Even still, there is some continuity, for instance, I would not accept that there is a "scientific" interpretation of the texts "until they're proven wrong." I agree with you, that's very God of the gaps. The continuity comes from an earnest observance that something eternal is being communicated beneath the mess of history, human purposes, and opaque lines, and that in itself can be quite beautiful.