"The way to falsify the hypothesis that the cuneiform tablet is intelligently designed would be to come up with a plausible explanation for a natural process that would account for it."
That wouldn't cut it. There is no way to prove the ID hypothesis for the tablets. What we have instead is overwhelming physical evidence that humans wrote it. We (rightly) concluded that the most reasonable hypothesis is that it was human produced. Then we TESTED that hypothesis. It was decoded and we know what was written on it. The Theory of Human Origins for the Rosetta Stone is now firmly established, not just because we can think of no natural process that could produce it, but because we have POSITIVE evidence it is a human artifact.
"Same goes for living beings. If their diversity and features can be plausibly accounted for, in accurate detail, through natural processes, then Occam's razor would take over from there, and ID would be falsified."
No, it wouldn't be. Even if we never uncover all of the physical processes might have been responsible, it still is a fact that there is no way to test for ID as an explanation for the evolution of life on earth. Unlike the Theory of Human Origins for the Rosetta Stone (THORS), which has positive evidence to back it up, we are still left with *natural processes can't yet explain it* as the only evidence for ID. As there is no way to test for it, it does not belong in the realm of science. As our knowledge gets better concerning the biochemical pathways, ID will have less and less place to work. But ID adherents will always be able to point to the things we don't know and say *Intelligent Design!*. It is at best a hypothesis empty of any predictive or experimental power. It is an argument from ignorance.
Are you honestly telling me that before we could figure out what was written on any of the artifacts we found, we couldn't be sure they were artificial?