Does an evolutionary model for the origin of the ur-flagellum predict that all the proteins diverged from their homologous counterparts at about the same time or that their divergence times are significantly different, depending on the amount of modification that would be needed to incorporate them into the flagellum? In my humble opinion, the answer to this question is obvious: there is no prediction here from an evolutionary perspective. The evolutionary model could only explain these observations, but it does not predict them. On the other hand, the molecular design hypothesis logically leads to the specific predictions described in the OP.
As you note, the theory of evolution only describes the mechanisms involved in the process of evolution. The theory can not take a genome and predict its evolutionary future.
However, I don't see how design makes the predictions you claim. An advanced race that stops by every million years and makes tweaks would produce the opposite pattern from the one hypothesized.