I’m not convinced that you’re not mixing concepts of FI here, but I don’t think it matters. As you point out, novel functions, domains, genes, and gene families do occur in specific clades. Regardless of the details of the calculation or the precise definition of FI, these represent the appearance of a substantial amount of functional information.
I would rather focus on larger issues that I think do matter. To summarize your approach, you are trying to determine whether the biosphere has sufficient probabilistic resources to hit upon functional targets, given the ratio of the target space to the search space. As a way of setting a upper bound on this ratio (i.e. a lower bound on FI), you use the number of bases conserved across long evolutionary time.
The major problems I see with your approach (which have largely been raised by me or by others already):
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Sequence conservation is not a valid estimator of the ratio you’re interest in. Conservation tells you nothing about most of the search space; it tells you only about the immediate mutational neighborhood of the existing sequence, which is a vanishingly small fraction of the total. More importantly, it does not give information about the number of nearby states that possess the function in question. Instead, it gives information about the number of states with higher function. (Higher fitness, actually, which need not be the same thing, but that’s a minor concern here.) But in standard evolutionary theory, the theory you’re challenging, adaptation involves passing through states with lower fitness (less functional states) until the local maximum is reached, and not returning to those states. Conservation cannot tell you whether there are less functional but still selectable states nearby in mutation space, and therefore cannot tell you anything about the size of the target space. This alone invalidates conservation as a proxy for the ratio you’re interested in.
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The target space you’ve considered consists of a single function, the function of the gene you’re looking at. To the extent that evolution can be considered a search algorithm, though, it is not a search for “the function performed by gene X”. It is a search for any function that will increase fitness. The only target space that will let you assess whether evolution could have produced some gene without design, then, is the space of all possible beneficial functions. Considering the probability post facto of achieving the function that did arise is indeed the Texas sharpshooter fallacy.
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The claim that only processes that incorporate design can generate 500 bits of FI has been challenged by two examples of two biological processes that observably produce large amounts of FI, in cancer and the immune system. Those challenges have not been addressed.