I doubt this will reach any ears given how empty the forums are but it's worth a shot.

I'm on Chapter 6 and I think that's long enough to have waited for the combat to click. It feels very frustrating to try and have Yagami do anything of note. Even when sending out basic attacks against the weakest of thugs, the first or second hit of a combo is nearly always blocked which leaves Yagami vulnerable to an attack. The only way to avoid this is to use Tiger, which results in a swift sucker-punch from the other goons. On top of that, it feels like every other hit knocks Yagami on his ass and getting up takes a lot longer than it took in the Yakuza games. In those games, there were even skills you could purchase to reduce the time it took to recover from hitting a blocked opponent. It feels like they're trying to make Yagami feel little more human and vulnerable, but that doesn't really play when dude can Spider-Man up walls and do crazy acrobatic throws like an angry Cirque du Soleil member.

Speaking of climbing walls, I've had a very hard time reliably getting Yagami started on a wall jump. Sometimes he'll wall-jump off of a static signpost in a way that feels impossible, and other times he'll bump up against the wall as if you had just slowly walked into it during non-combat exploration. Once you get up the wall, the tracking on his moves seems very spotty as well; sometimes he'll entirely miss enemies by going too short or too far, and many times the enemy will just dodge out of the way and hit you while you're vulnerable. if you try to aim it with the analog stick, he'll careen wildly away from everyone and splat on the pavement. This feels like the case for a lot of the advanced moves, too - for example, I've yet to hit a single enemy with a Leapfrog triangle attack, and that's not even counting the times I've tried to Leapfrog and Yagami simply chooses to instead get punched directly in the face.

If anyone has tips or tricks to let me know what I'm missing, I'd love to hear them. At this point it feels like I'm just going to have to grind block-breaking extracts and rely on those, because Yagami is so slow and so open to hits that almost every battle has two or three instances of him skidding along the floor like an epileptic, greased-up steak. I feel less like a crane and a tiger and more like a lame duck and Lil' Bub.

I pretty much exclusively used Tiger style through the whole game. Basically playing the same way I did with Rush mode in Yakuza games, quickstepping out of crowds and then picking off enemies one by one.
The sweeping hits of Crane style don't really make up for how weak they are, especially considering how spotty the tracking is on the heavy attacks. Although the Crane style EX Finishing Blow (spam triangle while in Crane style EX Boost) is very useful for thinning out crowds at the start of a fight.
Yes, the leapfrog, wall jump attacks and other context sensitive actions are spotty, so I rarely used those as well. Wall jumps are pretty useful for cheesing bosses though, if you find yourself in a pinch.

Quickstep and all the related skills have been my friend, like in Yakuza games, I stay mobile and always make sure there aren't any enemies behind me.

As for other tips, here's a couple of vital skills you could buy:
Knockdown Evasion or Reversal and EX Waking Wrath, these get you up from the ground instantly, so no need to tap X.
Re-Guard, familiar skill from Yakuza, you need to buy a skill book from one of the Dragon Palace casinos.
Flux Fissure is very good in the early-mid game, it one shots most weaker enemies if you nail the timing, and hits other nearby enemies as well. Downside is that they can block the hit, but you can pull it off pretty consistently by using it as a finisher to a rush attack combo.
Triple Finisher mixed with Charging Tiger (and Ferocity of the Tiger) lets you demolish your way through the rest of the game.

@briarpack: Thanks for the rundown! I'll probably stop using Crane, it definitely seems way too easy to get knocked out of a combo while using it and it doesn't hit wide enough to be handy. I've bought a bunch of those Tiger-only skills but haven't had a chance to use them, so I'll try and practice with those and see where that gets me. I've been doing a lot of grinding so I'm sort of thinking that I might just barrel through the story now. Judgment doesn't seem built for grinding combat in the way that the Yakuza games were. It makes me wish that they'd entirely reworked the combat to emphasize Yagami's different approach instead of just tweaking it from what Kiryu fought like.

Yeah the combat doesnt feel great, it gets better once you upgrade your combo speed to max but it's still a bit clunky. Rebounding off walls is never very reliable which sucks because conceptually it should be cool.

I dont feel like crane is useless though, it's not quite as OP as Majima's dance style was in Zero but it serves a similar purpose of thining out crowds whereas Tiger style is designed for stronger enemies.

At least the leveling system in this game isnt as needlessly convoluted as it was in Yakuza 6 & Kiwami 2. (Hiding moves in QR codes and books scattered across the city is a bit of a pain though)