i know you're not a big fan of reverse robins and i've come to not like the trope as much as i used to but something that's become noticeable to me now is that tim and dick often have next to no dynamic in reverse robin fics and it just makes me kinda sad. dick is either paired off with damian (understandable) or jason while tim is usually paired off with jason and sometimes damian. i don't think i've read any reverse robins fic where dick and tim still end up being close to each other despite tim not coming into the batfam as someone who idolized dick. i don't exactly want a reverse where dick idolizes tim as a plain reversal of their dynamic but if we keep tim's parents taking him to circuses and after they die he still visits circuses then he could end up at haly's circus on the night the graysons fall even in a reverse robins scenario. or maybe it's a scenario where tim does visit haly's circus as a kid with his parents years before and he meets dick as a new born. so instead of a picture of tim sitting on dick's knee, tim has a picture of himself as a kid holding baby dick. and then he visits years after and sees the graysons fall and it's the child he once held who is kneeling in blood under a spotlight. i dunno i think some og dynamics crossing over into alternate universes is sweet and even more so when everything else in the alternate universe is so different.
So I do agree and I’m going to give you an actual response but the first thing I wanna do is give a couple fic recs that I think are really interesting takes involving Dick and Tim with the reverse robin universe.
(Please Check Tags at least two of these are kind of heavy) 
Fic 1- Tim and Dick Cute bonding.
Fic 2- Not Happy but interesting
Fic 3- Really beautifully written while not super them focused the vibes are there
A lot of them are not Tim and Dick focused but I recommend checking the reverse robin’s tag and then looking specifically for the Tim and Dick platonic tag and you will find some super cool stories.
What I’ve seen that I personally like is exploring Tim, who either saves dick at the circus he is acting almost as Bruce and kind of takes him under his wing. One or two deal with the court of owls. I know for a fact, I’ve read one where Tim essentially talks dick out of killing Tony and either kills him himself or has helped Dick kill Tony. Depending on where you fall in the triggering/darker side, I might have a few more recommendations.
But a few of them that I’ve read there’s a really thin line between character bashing and criticism that’s happening, a lot of people might not love those. Said stories also really push the definition of what you can still consider a hero. I would pretty confidently say we’re not so much antiheroes we’re super villains… once again depends on your flavor of enjoyment! 
I am a really big fan of getting more Tim and Dick focused narrative! There are some truly awesome stories with it, but with those stories, I really think Jason and Damian are heavily favored, but that is literally because they are taking Tim and Dick’s place so it makes sense from the whole logic of following the cannon, but flipping it.
Before anyone gets mad at me, that is a fact, not my opinion. It doesn’t matter the actual character differences in personalities you’re putting Damian in Dicks place and putting Jason in Tim’s, so any story involving a Tim doing Jason‘s part end up being that relationship, heavy. Titan Tower AU, but Tim Drake version if you catch my drift! 
At least one fic literally gives us the Tim and Dick dynamic, but with it flipped. Dick is obsessed with him and following his every word almost to a problematic degree. No word of a lie Tim could’ve asked Dick to kill himself, and the boy would’ve thought about it. I will attempt to track that one down because it was fun.
10 out of 10 bringing more of the cannon, Dick and Tim into this AU would be amazing!! Their relationship is so sweet, protective, awesome, and everyone already knows I’ve made it a personal mission to spread my dick and tim against the world agenda.
So no complaints from me and Thank you for an ask that lets me rant about Dick and Tim!