Balancing Black Cleaver: A Page of Essence Reaver's Book

So, how to make Cleaver worse on assassins while still being good on Juggernauts and other tanky dudes?

My idea would be, take a page out of Essence Reaver's book:

Reduce flat CdR to 10%. Add unique passive: For every 40 bonus health (beyond Cleaver itself), get 1% CdR. Capped at 10%, for a max of 20% granted by the item. Maybe reduce total cost by 200 gold, or increase AD by 5.

Jugg items with 400 HP:

Assassin items with 400 HP: n/a