"Couldn't you do an experiment where you entangle two particles at different altitudes and measure to see which one drops faster?" Yes. The experiment is easy

"Couldn't you do an experiment where you entangle two particles at different altitudes and measure to see which one drops faster?" Yes. The experiment is easy to run. The equipment that can detect the factor-of-10^-50 percent difference between them is not so easy to come by. The problem with quantum gravity is the lack of data brought on by the fact gravity effectively doesn't exist on Earth at what we typically call "quantum" scales, compared to the overwhelming influence of electromagnetism and the nuclear forces. (The inhabitants of the Dragon's Egg in the science fiction novel of the same name, which are creatures made out of matter on the surface of a neutron star, presumably did not have such troubles making a theory of quantum gravity, because they could gather data directly. We creatures made of atoms in an environment that permits that are not so lucky!) It's not that hard to come up with situations where you get less-than-Planck time expected differences in behavior. This is another frontier in science nobody knows the answer to. For as small as Planck time is, there are ways you can theoretically detect if the universe was "rounding" at that scale, and so far they have all consistently come up as "nope, the universe isn't rounding"... yet it is also almost inconceivable with modern physics how it couldn't be in one way or another. (The most interesting one was trying to pick up various effects of such quantization on photons travelling so far across the universe that the differences would be detectable.) There are still many mysteries!