So, Melee Carrys have an innate problem with just how they exist, but I think if we change some things about Yi, you can alleviate the problems he already has.
The Passive has been reworked so it'll be up everytime you gank. With an attack speed of 1.0, you'll always get off more double strikes than before (Unless you have over 2.33 attack speed, which you probably shouldn't anyways). This basically serves consistency purposes master yi has.
Q hasn't really been touched much. Although there's no place to put it, increasing the animation speed would be better, just in terms of control. The percentage and damage change also serve consistency purposes.
W has been remade to improve viability. AD yi rarely uses it, and it is a cornerstone in AP yi. I increased the AP ratio more than it is now to make up for the shorter duration and the armor and magic resist nerf. However, the lingering bonus stats will make it so AD Yi actually has a use for it.
E has been remade for additional on-hit magic damage. The only real point to this was to improve AP Yi. There is a slight damage nerf, but its eventually made up for in magic damage.
R has increased movement speed and increased attack speed at earlier levels. In addition, he isn't vulnerable to attack speed slows, so randuin's and frozen heart won't completely cripple him now.
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