Genetic drift is not only actively observed in populations, but through rational thought and a bit of math you can see it is predicted to occur. I'm afraid most creationists don't even know what genetic drift is, but if they do they would agree it is real.
Natural selection is also actively observed in populations and predicted to occur. Creationists likewise (sometimes only if pinned in a corner) will agree that it is real.
So what's your beef?
Logically, why would crossing one boundary (phyla) require anything different that crossing another boundary (species)?
Golly, why don't you go off for a few months and read some books?
Unless the population size is quite small genetic drift is sloooow. It dithers about here and there and takes forever to get anything done. Then when mutations occur the new alleles/genes/chromosome arrangements/etc. occur among a small number of the population. If natural selection is not present to give these novelties a boost genetic drift has the tendency to just wipe them out. In general genetic drift is the enemy of innovation.
Most major evolutionary innovations have taken place following mass extinctions. These events leave many niches wide open. Examples are the Permian-Triassic extinction, which allowed the evolution of dinosaurs; the Cretaceous-Tertiary extinction, which allowed mammals to replace the dinosaurs; and the late Devonian extinction, which was followed by the development of all modern types of plants. Some people think that the Cambrian explosion followed a Vendian-Cambrian mass extinction. The rapidity of these developments indicates natural selection was the driving force. If we waited for genetic drift to modify dinosaurs into birds we'd be waiting forever.
Remember that it is impossible to consider evolution as solely based upon natural selection or solely based upon genetic drift. Leaving out either gives a picture that is inaccurate.
And no, your thunderstorm analogy has no resemblance to reality. Mine is a much more accurate analogy.