Critical Strikes
Many people have already complained about critical strikes before, and offered several solutions to fix the system. The link I attached was a rather creative solution, but would remove crit from the game. Crit is an important part of the game, so it should not be removed even if there were other ways to increase DPS to compensate. Anyway, here is my idea. I hope you enjoy reading and I would love to hear your feedback.
Every autoattack (not procced by abilities that apply on-hit effects), the "crit counter" is increased by the user's crit chance. At 100 stacks, the user critically strikes, consuming 100 stacks. If the user is out of combat for 8 seconds, the crit counter is reset to 0 stacks. If the user has less than 5% crit chance, the base crit damage is only 125%. If the user has less than 15% crit chance, then the base crit damage is only 150%. These changes would remove the RNG from crits while preventing the system from being abused in lane by taking 1 crit chance rune. If you actually build a crit item, however, your DPS will not be affected by the countermeasures. There is also one item-specific change I propose.
Statikk Shiv:
Unique Passive: The crit counter is not reset while out of combat, and is charged by movement.
Unique Passive: Whenever the user critically strikes, 50 magic damage (25 damage, but it always crits) is dealt to up to 4 nearby enemies, prioritizing champions. This damage scales with critical damage (i.e. Ashe will do significantly less damage early, Yasuo will do slightly less damage, Infinity Edge will increase the damage)
These changes would maintain the item's identity, while also making the passive easier to manage with the new crit system. The crit counter being charged by movement would allow for more burst at the start of a fight, which is why this item is usually bought (also helps with waveclear and the lightning increases DPS). As this item would be proceed more frequently, the magic damage is nerfed in compensation.
I don't think Phantom Dancer, Infinity Edge, Youmuu's Ghostblade, or Trinity Force would need to be changed.
Edit:
After more thoughts on Tryndamere, I believe his base crit damage would have to be changed to 155%/170%/185%/200%, upgrading with each point of his ultimate that he has. The nerf could be compensated by other buffs, but would be necessary as he could absolutely dominate in lane if he could time his crits while trading.
I also removed the changes I had in mind for Infinity Edge.