I'm not a physicist, but it was my understanding that pilot-wave theory and Copenhagen QM make identical predictions (each is a mathematical reformulation of the other). If that's true, then how could any experiment favor one over the other?

(Each lends itself to a different set of intuitions; maybe one of those sets could prove to inspire better hypotheses for research?)

this isn't theoretical, but is a nice visualization of the ideas behind the pilot wave/particle system

https://www.youtube.com/watch?v=nmC0ygr08tE

the plot at 1:40 is where my mind was blown.

Where is the experimental support?

I think this is the paper, which is very briefly mentioned: http://advances.sciencemag.org/content/2/2/e1501466.full