1: They can't measure gradients because they can not "feel" another particle except via gravity. You can only measure a gravity gradient by comparing it to another force, but they have no second force to compare to.
2: They can't see redshift because they can't see photons at all.
3: They can't see gravitational waves for the same reason as #1, to see a wave you compare two particles (distance in current experiments), but they can't do that, any comparison would be via gravity and would be affected identically, so there is nothing to compare with.
Interestingly pure energy only experiences gravity (I don't means photons, I mean simply energy, that "thing" which is conserved).
Which is why I personally think dark matter is simply energy, there is no extra particle. The only question is what form does this energy take.