Summary
For the unfortunate case I’ve been unclear, third and last try: I very strongly believe the Mongol stable is better than the Persian one in castle age. See for the original post The Cuman Kipchak - An Analysis and for the second post The Cuman Kipchak - An Analysis. I do my research, I know my stuff. 
For complete disclosure, I also read Cysion’s text about the Franks in the past. Who isn’t interested in knowing what he thinks ? A shame he is mostly a reader though (cf. https://www.aoezone.net/threads/are-there-really-any-devs-around.165629/#post-668574).
There is now one third of the users in this thread who have expressed outright support for the idea of the elite kipchak getting a careful and reasoned buff of +1 atk or something similar, which is very nice in my view. Me, for starters, but who am I?
Much more importantly @walkop (obviously, as it was his idea to begin with, mine was originally bracer), (last supported here: The Cuman Kipchak - An Analysis, “I’m still in favor of +1 to all Cuman CA in Imperial Age”); @LyricLight76377 (The Cuman Kipchak - An Analysis, “kipchaks need 1 more dmg”); @Pulikesi25 (The Cuman Kipchak - An Analysis, “it might be good to give a small buff”); @CheshireWig3203 (The Cuman Kipchak - An Analysis, “[kipchaks] have no damage output in imp”); @UncannyPlayer22 (The Cuman Kipchak - An Analysis, “Elite Kipchak needs something like +1 attack to make it more impactful late game”) and @phoenix1089 (The Cuman Kipchak - An Analysis, “the only reason kipchaks need a dmg buff is due to”).
@JoJo9942 liked my last post arguing for the said buff, so I suppose his state of mind shouldn’t be too far apart of mine on this question.
Others, without directly writing a comment in this thread, shared their support through a like, for instance @TougherTrack508 to name one.
And others don’t see it as too big of a change, like @CactusSteak2171, who wrote something with which I totally agree: “I wouldn’t say [+1 atk to the elite kipchak] will them make OP, but that it shouldn’t be decided based on the belief that a civ needs to just spam its UU all game long.”
Others are in a comparable position (cf. The Cuman Kipchak - An Analysis and The Cuman Kipchak - An Analysis).
I also agree with @Lonezwiebel when he says that “Kipchaks carry Cumans like Mangudai Mongols.” and “Like every player, they play with Cumans, they go for Kipchaks, more than Knights and Paladin and that tells a lot.” (The Cuman Kipchak - An Analysis), which is precisely why I’m focused on the kipchak.
Perhaps we could all agree that it’s worth giving it a try? The elite kipchak would have 6+3 atk for his main arrow, only one without bad accuracy. For the very remote possibility that the experiment nonetheless became an absolute catastrophe, changing it back is still possible. 