My biggest problem with "new Zac" is that he seems like he's all over the place in terms of what his "role" should be. Old Zac had a clear identity: Dive the enemy team really hard and cause a bunch of chaos, knocking people around while sustaining through damage by scooping up blobs. New Zac has a Q that requires him to hang around teamfights (immobile) while slamming people together and an R that requires him to stay immobile so that he can grab and carry one or two enemy players to a disadvantageous position for them. The reason this feels so disjointed is because Zac's Passive, E, and W, which were unchanged, work on the premise that he can move about and collect his blobs, which the new kit does not allow him to do because of the new Q and R which root him in place.
Because of his "stand and fight" feel, his Q, W, and E essentially hurt him with very little chance for him to actually pick up his blobs and heal himself to sustain through a fight. As a self-hurting tank with no personal shielding, his blobs are his only means of surviving a long engagement. With the new immobility of his kit, it makes it much easier for enemies to counter-harass and harm him simply for using his kit as intended since he'll be standing in place unable to fight back.
Then there's the matter of his E and R. His old E would knock foes up for one full second, which was usually enough time to use a W and chain into R, which would knock the enemy to a disadvantageous position which is what the new ultimate does anyway. Then, he would get a 50% movespeed boost, and could use the extra bounces to knock teammates away from the isolated target, making Zac amazing at breaking the enemy apart and setting up allied Assassins and Bruisers that don't have strong AoE power, while also balancing the team out by providing some AoE damage through his W that was set up through the blob generation from his R (and mid-R W casts). The new ultimate is unreliable to land unless the enemy is out of position already and has to run through Zac, or unless Zac has someone else helping him lock them down. This takes away from his identity as an initiator, as instead of safely setting up his team to come in he basically has to have someone set him up so he can safely use his kit.
When I was reading about the then-upcoming Zac rework, it was noted that it was being done (along with Sejuani / Maokai) in order to create an identity for the champions and separate them from an "Amumu feel". Zac NEVER felt like Amumu to me, and I've played Amumu plenty. Amumu would use his Q, then use his R to lock everybody in place, then stand on them with his W and spam his E until enemies were dead. Zac, on the other hand, constantly had to move around the battlefield picking up blobs and had to be careful on his bounce placements with his R or else he would possibly move the enemy into a position not ideal for his team. This required a lot of thought and balancing between "Do I go for blobs for healing / damage" or "Do I go for positioning to line up an enemy for a skill shot for my team". He already had an identity. I don't know how anyone could think he didn't.
Speaking of his E and R, by the way, Amumu's Q guarantees a landed R. Blitzcrank's Q guarantees a landed E, followed by R. Thresh's Q lines up with his E perfectly as well. Tons of characters are built around "land this one really hard to land / risky skill and be rewarded", and yet Zac, who has a self-damaging skill that puts him in danger if he doesn't land it, can't get a guaranteed Ult because... why? Because Lee Sin is the only one who can Q -> Q and land a guaranteed R because it looks flashy, knocks them farther back than Zac can, and does way more damage than Zac does even if Lee Sin builds tanky? This mentality of "We don't want to guarantee his R" makes no sense to me when compared to the rest of the champion roster.
My recommendation? Revert the changes. I'm normally happy with most of the reworks, but this has completely neutered Zac. Everything in his kit has its own identity and feel, and none of it goes well. I mean, look at this mess:
Q: Slow that leads to an empowered (range-wise) auto-attack that causes CC for a slight duration. Roots Zac in place. Generates 1 blob despite being "two casts", and works well with Lich Bane / Iceborn Gauntlet / Trinity Force. Items that Zac will never, ever, EVER build.
W: Deals damage and reduces cooldown on itself by picking up blobs generated from all abilities. All other abilities root Zac in place so he can't walk around and pick up blobs.
E: Hard to land skillshot that used to be very rewarding because it could chain into a W->R which allowed him enough blob generation to survive teamfights and be aggressive. Now so unrewarding that it chains into nothing. No reward? Why take the risk, then?
R: Zac "stuns" himself and starts channeling, becoming "immune to CC". What do we call a Zac that doesn't move from a single location, can't pick up blobs, has to wait around while doing nothing to the enemy, and has no way of dealing damage no matter how long he channels? A sitting duck, that's what.
If you're not going to revert the changes, here are my recommendations:
Passive: Give him 50% increased move speed after he picks up a blob for 1 second. That should give him some mobility he needs when he's outside of his ultimate.
Q: One blob upon landing the first part of the Q, a second blob for landing the second part. Allow him to move while doing the second cast.
W: Keep this the same.
E: Revert the 1.0 second knockup. This was just crippling and insulting.
R: Give Zac some damage reduction at the very least! He's a sitting duck that anybody can burn into the ground during his ultimate! It's so risky that snap-casting is the only appealing way to use it, and snap-casting it makes it feel like a lame version of his old ultimate!
This may read like "Man, Zac will be a CC monster that's hard to pin down", and that's what he was before and he still didn't see a ton of play. Why? Because he's a self hurting tank. It made him risky to play, and even with his old E and ultimate he wasn't overpowered at all. Sure, he can sustain if he can get his blobs, but that's the problem now: He can't get his blobs anymore, so he went from a viable tank to the Urgot of tanks.