Yes, Gried is a possibility.
But as you said its better avg dmg, so u lose some max dmg.
Also, you lose the +30 Attributes off Botd, therefore the 40/9 Dex would not help you necessarily gain any dex, maybe even lose some.
Then you would also have to put 30 more into strength to use e cara, and lose 30 Vita.
Overall i believe Botd>Grief.
Lastly, this build doesnt include any Ladder Runewords