Ovinomancer
No flips for you!
So you claim that there's no granular timing and then go on to talk about granular timing. Uncanny dodge triggers sometime after "the attack and damage is determined" but before "the damage application." Generously reading "the attack and damage is determined" as synonymous with "If a hit, apply effects," I'll go ahead and add the other to the timeline.
Uncanny Dodge: Make an attack --> If a hit, apply effects --> Uncanny dodge triggers off the hit and halves damage effects --> "the damage application"
And we're back to separating the application of other effects from the application of damage, and then this contradiction:
UD vs shocking grasp: Make a shocking grasp attack --> if a hit, apply lightning damage and prevent reactions --> no UD because: can't react --> "the damage application"
The problem with saying that there is no granular timing is that there is inescapably a sequence of events, no matter how implicit, to make the action of the game comprehensible. The phrasing "On a hit, you roll damage" makes it clear that the check for attack success happens before the roll for damage and the application of effects* ("Basic Rules" 73). The triggers of reactions actually discern between these different stages in the sequence of the attack. Uncanny dodge could easily trigger "when you take damage" and still reduce that damage. How do I know? Absorb elements is a reaction that does exactly that. But uncanny dodge's trigger is something else, "when you are hit." Note that there are also reactions triggered by distinct actions, such as casting a spell in the case of mage slayer or attacking your ally in the case of sentinel, and these occur after the trigger, which is in these cases the full action and not some stage within it.
*I would go so far as to say that in every case "On a hit" is a conditional for gameplay sequencing, essentially shorthand for "If the attack succeeds, then Y," but not an assertion of in-narrative simultaneity. "When you are hit" is used in such cases, where the "you" is clearly not the player but the player character.
There's only a contradiction if you insist on a formalized timing. There is no formalized timing in 5e, just the statements that reactions occur after their triggers unless they say otherwise. Since Uncanny Dodge does not say otherwise, it occurs after the hit is completed. Since shocking grasp prevents reactions on a hit, you cannot react to that hit (except with shield, which specifically says it interrupts it's own trigger and can negate it). There, no timing charts and everything works just fine. It's only when you apply a strict order of events that's absent in the rules that you end up with your contradictions.