I am trying to picture how electrons move around in atomic orbitals Are they thought to continuously pop in and out of existence at various points inside the orbital defined by probabilities or do they follow definite paths that are made fuzzy by the Heisenberg uncertainty principle?
I sometimes find myself as thinking of the electron cloud as a gas with varying charge density corresponding to the shape of the atomic orbital.
I think you miss an important notion to get a better understanding of the behavior of the electrons: wave-particle duality. I believe that a better visualization takes into account that you have to deal even with a wave. From what you say it seems that your picture is shifted only to the particle-side,  keep meditating for a half an hour trying to visualize the electron as a wave. For me is a very interesting mind experiment. Then move to the orbital concept. 

At Lund University researches took a picture of a moving electron. This image maybe could be helpful for your meditation:



Lund University. "Electron Gets Film Debut In First-ever Video Of Its Kind." ScienceDaily. ScienceDaily, 25 February 2008. www.sciencedaily.com/releases/2008/02/080222095358.htm.