There’s a reason I wrote “most zoo decks”. But still, the problem here is that you are a Zoolock with an empty board. You should not be having an empty board when your opponent can drop a giant.
Looking at this list, most of the cards you named would be a no for me. A lot of the cards in this deck can be dropped on the board unconditionally. You don’t want to add too many cards that sit in your hand. Soularium also means you have to be able to play the cards you draw (at least most of the time).
Keep the Thrashers. They’re not only here to proc your Vulture, but they’re also amazing at hitting face or making favorable trades. For 3 mana, they are pure value, especially if you can curve them into a Vulture. As for healing, no. This deck has to burn the opponent down fast. Your mana curve stops at 4, so healing is not the deciding factor against control. If you lose steam, you need to cross your fingers and pray for Soulfire.