I fear you are going about this in exactly the opposite sequence of evaluation and assessment. Here you are attempting to dismiss Evolutionary evidence, because, from the start, the data points don't seem to be provably connected.
But that's not how any of this developed in real time.
Hypothetical Sequence for Explication Purposes
1st: Academics aggregated large numbers of finds, with information about the sedimentary rock layer they were found, and where.
2nd: they started to arrange the information in order of Younger down to Older, with no major effort to fix exact chronology as of yet.
3rd: Looking at the world's collection of fossils, from Younger (More Recent) to Older, they saw a strange phenomenon: mammals with which we were familiar in the modern era eventually disappeared the deeper into the layers academics reviewed.
4th: As recognizably modern fossils began to disappear, variations of these animal designs would appear... and then continuities between these variants began to be seen, where Variant "Z" and Variant "Y" might dominate one layer of rock - - while beneath "Z" and "Y", on levels below them were found Variant "X", which had commonalities to both "Z" and "Y".
5th: This process repeats itself all over the world, with similar findings for all major categories of creatures that left fossil evidence.
6th: What was noted was that below the level where "large mammals" seemed to emerge from out of nowhere, scientists found that "large reptiles" seemed to come to an end.
The Big Picture:
So, Darwin and his like-minded investigators were compelled to make some general conclusions:
a) Over very long periods of time, categories of animals showed changes, where frequently it was seen that some types of animals completely disappeared, while other animal types would emerge to take their place.
b) Modern researchers refined their deductions over these transitions until they reached an amazing conclusion:
..1] Large mammals couldn't become populous until large reptiles had vanished.
..2] Until we knew more about genetics, "species" tended to be defined based on the aesthetics of their shape and form.
..3] There was a "Time-Context" factor applied to the term "species", even though it was quite possible that a more recent animal form may be literally the grandchildren of a completely different looking animal millions of years before.
..4] The key factor to emphasize regarding changes-over-time is that populations could either completely go extinct, or changed so dramatically it is only possible to know if examples of prior phenotype populations did not go extinct by finding two divergent subsequent fossils populations that share different aspects of the earlier (potentially "common ancestor") population.
@Daniel_Fisher, so with these observations and conclusions in mind, what exactly would you like to object about or refute?