So I’m guessing the real sticking point for you in my color analogy is the “information brought to us through our senses” business.

No, the entire argument is a false analogy, that's the sticking point.

The feelings that colors induce in us are no more arbitrary or nonsensical than the perception of pain.

I suppose one could overreact to those feelings, but so what? That sounds like a mental health issue to me.

But let's turn to your second analogy. At least it has the appearance of relevancy:

Now, you can define that mysterious something you call "transcendence" anyway you want. And if that isn't arbitrary and nonsensical, what is it?

But you can't define "justice" anyway you want, because its definition is informed by real world experiences:

"Justice" is derived from the adjective "just" (a value judgment).

Our sense of justice is a complex set of value judgments that generally reflect universal values, but can be idiosyncratic as well.

Value judgments are by nature relative, but relative doesn't imply arbitrary or nonsensical, and that's where your analogy falls apart.

(Also, value judgments aren't definitions!)

So, even if we disagree about particular judgments, we know what we're talking about when we say "justice."

On the other hand, no one has any idea what they're talking about, when they say "transcendence." So your analogy fails.