The words in the Constitution and Amendments must be given the meanings they had when ratified. In other words, since meanings change over time in a living language such as English, we cannot arbitrarily apply 1868 meanings to words used in 1789, nor vice versa.
I don't know if this is what you intended to say, but my view is that when the 14th amendment copies a phrase like "due process" directly from a portion of the Constitution that was written in 1789, the 1789 understanding of the phrase should prevail. In fact, I would even go so far as to say that the entire Constitution, in all of its amendments, should be understood more or less from a 1780's-type standpoint (except in cases where a word clearly has a more modern meaning), and that it's the responsibility of those who draft amendments to make sure that their language is largely consistent with the language that went before it. In other words, the Constitution should read like a single document as much as possible, rather than just a collection of laws.
There may come a time when the language of the Constitution becomes substantially less comprehensible as language evolves further, and at that time, it may be necessary to pass an amendment "translating" the document to a more modern dialect, though I can just imagine the can of worms that would open.
No. While the words "due process" appear in both places and absent specific internal language that they were actually copied from the first place, they first have to be given their meanings according to that understood at the time they were used. To assume they were "copied" means that judicial construction is already being applied before a determination of ambiguity, which enables construction to be used. A Catch 22? No. Construction cannot be applied until after ambiguity is found de novo.