Instead you simply have to deal with towers of abstractions, understand the experiments. It is counter-intuitive to claim we also couldn't see photons, but really, the disconnect between theory and phenomenology is rather large. I guess we are only really interested in the weak-electromagnetic force. And that's a probabilistic theory thanks to quantum mechanics. Discrete systems are macroscopic simplifications for didactic and deductive reasons.
Gravity is next to the other three basic forces. That's a simple dualism. So time stands still for the photon, but space bends. And we can't fully explain how.
And don't get me started on infinity. It's just a number big enough for all intents and purposes. Conversely, it's pretty simple to think about the opposite: Nothing. So if you you take an infinite amount of time to observe a clock at light speed from your inertial frame of reference, it will just not move at all -- there are no "2 ticks". Corollary: A photon doesn't experience time at all. And this holds in quantum mechanics, because a photon doesn't exist until observed. A photon is thus the measure of interaction, a delta on our clock. Colloquially, time is the order of events -- if nothing happens, time stands still.
For sake of the argument: If you just switch the photon and observer in your example, the photon in infinite time wouldn't "see" any time pass on the outside observers clock. He wouldn't move. But this is just too simplistic, you have two points in space that practically can't move, because they don't
From the frame of reference of a photon, the environment would
> 2 ticks on a clock (ΔT) at c, take an infinite amout of time in the reference frame of an ordinary observer (Δt).
Extending the thought, you are trying to multiply infinity by infinity. As you said, we cannot handle infinities. I guess that is because there can be only one, one singularity, one universe. That's why the speed of light is set at unit-interval.
