There is so much that I like here and so much that I don't like here.
Forbidden Idol is so good for ER because it provides ER's mana regen passive and its CDR. Idol being in the recipe allows AD's to pick it up in the mid-game for some extra mana regen and CDR.
However, Reaver's mana regeneration passive should replace Idol's passive mana regeneration to promote the interaction that Reaver's passive provides. I think Essence Reaver would feel a lot better if the passive was emphasized over passive mana regeneration.
Likewise, ER's passive I feel should apply only on auto attacks like live ER does because there are a lot of abuse cases for this item that could come out of applying on all physical damage. What's to stop someone like Talon or Pantheon from simultaneously harassing and clearing minion waves at the same time for essentially no mana?
Pickaxe vs. BF sword is a tricky place to look at because it depends on when the item is supposed to be purchased. It really doesn't matter unless the item is tied to a particular AD value.
Vampiric Scepter is something I don't currently like on live Essence Reaver, and is something I don't like on it here. Vampiric Scepter makes it compete too much with other lifesteal items like Bloodthirster and Blade of the Ruined King. Removing it and adding more power elsewhere allows it to compete with the needs of the player instead.
Live Essence Reaver begs the question "which lifesteal item do I want?" Essence Reaver should ask the question "do I want mana regeneration on my AD build?"