I have a feeling you just want to complain. Coil and Crystal Tower are horizontal story and we already have quests in regard to the U tribe. Beastman quests are also a huge source of horizontal story. Heck, so are EX Primals. There are sooooo many of what you want if you'll stop and smell the roses.
I get what you want and thats fine to want more of but we have it already.
I appreciate you defining these terms for me, but I'm afraid your logic looks faulty :x You rule out CT as being horizontal because 'it has a starting point in the original story' (I assume because it includes Biggs, Wedge, and Cid?), but so would many of your suggestions for horizontal story lines.
It sounds to me like you want more side quests (I agree, who wouldn't? :P), but your request is bogged down by semantics. Many of your suggestions sound great, but I find the horizontal vs. vertical structure makes it hard to understand what your real point is. I don't really know what makes your requests different from the story lines we already have.
Basically he wants sidequests about the things he requested and everything else that already exists "doesn't count".