Kat needs something done but this is not the answer.
I'm a Katarina main and I understand the point behind these changes/nerfs. It's not that she is broken but more so that the enemy doesn't feel they can do much when it happens so fast. I see that these changes are aimed at slowing down how fast she rotates down kills with more risk and options but with much less burst. But this is not the right way to do it.
See the problem about these changes is that they remove a lot of her ability to lane. Forcing a player to have to shunpu enemy champ on trades straight up nerfs half of her lane match ups. Take Zed or Syndra for instance. You do not want to shunpu them directly on a trade but near them. When a zed uses his combo you want to e a minion near him, q/w him, and run away without ever getting in his e/AA range. Now Syndra is similar in a way. She can reposition her q you dodge and slap it right on top of you. When you shunpu a minion near her it allows you to utilize that movespeed to dodge that incoming reposition ball. If you are on top of her it is much harder to dodge. The issue with that is that if you lose these trade potentials you will never be able to trade. I'm not even going to go into the issues this kit will have towards mid to late game when she can't get any kill gold or minion gold early on.
The main issue with Kat is her mid to late game with resets in fights. Nerf/change her appropriately where it matters. Resets has always been something near impossible to balance without it making the kit extremely weak(and that is exactly what you are doing, nerfing her kit damage potential to balance the resets).
***There is a really simple fix here. ***Make resets apply a 1 second cooldown. Kinda like how MMORPG's have a global one second cooldown except make it only on each move and allow it to stack/decay over time(doesn't have to just an idea if you did want to nerf the damage). She wont be able to just throw 3-4 bouncing blades all proc'ing the second proc on each hit and just demolishing an enemy team in less than a second. Kat would have to play it correctly and utilize the move speed more for positioning than damage on each kill(the w). The enemy would have time to respond well. They would actually be able to react in time. Dfg is going to nerf the cheese dfg/e/q/w/r kill 1-2 people zhonya instantly. She doesn't need damage nerfs. Kat is a burst aoe mage assassin, this isn't the issue, instant resets are the issue.
TL:DR Resets are the real issues. Add a second cooldown on each move after resets like how global cooldowns work in MMORPG's but on each move separately.