Do photons experience every moment in time and position in space simultaneously? Would it be more correct to say that a photon, traveling at the speed of light, would experience all points in time simultaneously, and therefore be everywhere at once?  It might be just our perception that seems to portray them as moving?
 A: A photon traveling at speed of light has a lightlike worldline. It has one place of emission and one place of absorption. The spacetime interval between both points is empty (=0), that means that no spacetime is between them. That means, if a photon would experience something, it would experience both points as simultaneous. But there is no reference frame of photons, photons don't experience anything.
Concerning the points of the worldline between the place of emission and the place of absorption, they correspond to the empty spacetime interval between the point of emission and the point of absorption. For this reason, from the hypothetical point of view of the photon only the point of emission and the point of absorption would exist.
This empty spacetime interval corresponds only to the hypothetical point of view of the photon. In contrast, all observers perceive the light wave as moving at c. By consequence, and as you are suggesting, the movement at c is not more and not less than an observation. This fact is also taken into account by the formulation of the second postulate of special relativity.
A: 
Do photons experience every moment in time and position in space simultaneously?

No. LIke WillO said, photons don't experience anything. 

Would it be more correct to say that a photon, traveling at the speed of light, would experience all points in time simultaneously, and therefore be everywhere at once? 

No it wouldn't. A photon is emitted from say the Sun, and it travels through space to your eyeball, which it enters 8 minutes later. 

It might be just our perception that seems to portray them as moving?

No, they really do move. 
To understand all this, imagine you're travelling at the speed of light. As it happens matter cannot travel at the speed of light, but just imagine you're moving so close to speed of light that nobody can tell the difference. Anyway, you might think you experience all points in time simultaneously, and therefore you're everywhere at once. But you aren't. Let's say you're travelling through space on some prearranged course, and I've hacked your system in advance to find out what it is. I could stick some big old rock in your path, and you wouldn't see it. BANG, and that's the end of you.  
The thing to appreciate is that when you're moving at the speed of light, you can't see, and electrochemical signals aren't moving in your brain, so you can't think. Light would have to move faster than light for that, and it doesn't. So you don't see anything, or think anything. You don't experience everything. You don't experience anything. 
