Why not just rework crit into a charge build-up system?
Instead of a semi-RNG % chance system, why not have it act similar to Shiv? Like this:
Upon attacking, add your crit chance to a hidden number, let's call it X. Then, check if X is greater or equal to 100. If it is, subtract 100 from X and have that attack crit.
So if you have 30% crit chance, the sequence would look like this: X=30>60>90>20>50>80>10>40>70>0>repeat Attack damage=200>200>200>400>200>200>400>200>200>400>repeat
If 10%, like this X=10>20>30>40>50>60>70>80>90>0>repeat Attack damage=200>200>200>200>200>200>200>200>200>400>repeat
This would allow a much higher skillcap to crit, and would make champions who are based around crit like Tryndamere less frustrating, so it feels like you lost to Tryndamere, not RNG.