Hi, fellow asexual here.
I didn't read through every post, but just wanting to comment on the label of the relationship and how they refer to each other. I don't think there's a standard answer to either question.
I think there's a grey area between a V and a triad, and which label to use depends on your criteria for an intimate/significant relationship. Some people think sexual behaviors mark a significant relationship, and others think the emotional component is more important. I'm in a triad that some people may categorize as a V, because not every two-way connection among us is romantic (not to mention sexual - we're all on the asexual spectrum). But to us, triad is a more accurate label, because the emotional intimacy is equal among all three of us. We don't think whether our feelings are romantic or not is very important.
As for how to address each other, that's even more flexible. The labels we use in our triad include SO, romantic friend, and affectionate friend. We also simply refer to each other as friends under some circumstances, because we're the relationship anarchist type kdt mentioned above. I'd say the two guys in your story are friends or "special friends." But as kdt said, don't let our answers restrict your creativity!
BTW, I like the idea of having the two guys have a non-romantic, non-sexual, yet still highly intimate relationship.
It's also possible for them to love each other romantically but not sexually, because one's romantic orientation and sexual orientation don't have to be the same.