It seems to me that in the second syllogism, as well as in the former, the
first premise contains 2 terms in "EITHER 'caused' OR 'random,'" in which
case the syllogism could be considered illogical via 4th term fallacy.

However, regardless of whether or not the major premise is flawed (& all
semantics aside), this has certainly been an interesting thread, & I've not only
enjoyed the discussion, but very much look forward to more in the future.