If one were to store copyrighted data (text, images) in a manner that was unrecognizable compared to the original, but that could be used to recreate the original, does that violate copyright law?

There are a few problems here. First of all, you are clearly attempting to circumvent copyright protection. There doesn't seem to be any other purpose for this scheme. But beyond that, the creation of the database is forming a derivative work. Derivative works cannot be distributed without permission of the original copyright holder. Further, one might question whether your database is eligible for copyright protections on its own, given that it is factual, not original. So anyone could steal your database (although still not be able to distribute it themselves, since that would violate the copyright of the original work; in fact "stealing it" from you is making a copy--which is infringing). Your plan to display this in a browser by recreating the text through javascript access to the database is, in fact, distribution of the original text. You have gone through a very fancy way of reproducing the original, but any judge is still going to point out the obvious: you are publishing the book in competition to the original. But, even if this workaround were legally justifiable, you would still end up in the situation you are trying to avoid: getting sued. Sure, with legal justification you could win, but you would STILL have to pay for the trouble of a lawsuit and suffer an injunction on distribution while the multi-year legal process played out. There are clearly grounds for a lawsuit because it involves someone else's book. There is no way to avoid that element of this situation. But, as I said, what you are intending is clearly illegal. You would lose a trial if it came to that.

If you "recreate" you "violate".