Update: I've been playing this deck exactly as it is in the mainboard and while there are many games where it just fails to find an essential piece in time, the also many games where it does work makes people SO MAD! It's great! They never get to do anything and then all of a sudden I have a million zombies. Just try to get your utilities online ASAP and stall as much as possible until you get more and more pieces to increase value until everything is virtually free. They can have their creatures, just make sure to tap them down with Fan Bearer and Binding Mummy with Verity Circle out, or block if you need to with Zombie Infestation tokens at a bare minimum replacing every card you can with Cryptbreaker and Liliana's Standard Bearer's card draw abilities. If you have extra mana, opt to use Cryptbreaker's token generation in most cases early game to conserve cards.
Once you get Anointed Procession, or an additional Verity Circle or Binding Mummy you're set, but a Fan Bearer can often fill that slot enough to win games, or Cryptbreaker instead of Zombie Infestation but I'd say that's less common for some reason.
I've been working on this Binding Mummy + Verity Circle
combo, it doesn't feel Tier 1 competitive but it definitely has potential and is a fun payoff.
The combo is Binding Mummy + Verity Circle + Zombie Infestation
which provides fair value on its own but with an additional Circle or Anointed Procession allows you to draw and discard card to make zombies instant-speed indefinitely as long as the opponent has a creature to tap down. If necessary, a second Binding Mummy will work too but all three cards provide a slightly different effect and I would say this is the least desirable option.
The deck probably needs Grim Tutor, but I'm not sure. The only real challenge is getting all the combo pieces, and you often can spare the mana if you land Infestation because that represents a blocking threat anyway, but Liliana's Standard Bearer might just be a better use of that mana considering it is instant speed and provides card draw in case you have to generate those chump blockers early using your valuable card resource.
Awaken the Erstwhile is a fun one, and while it may be hard to resolve against control, it's kind of great to have against creature-light decks. Say you have Binding Mummy, Zombie Infestation, Verity Circle, Anointed Procession.. if you cast Awaken the Erstwhile, each player discards their hand, you make double tokens, tap all their zombies to swing in with any zombies you already had in play, re-draw a card for each zombie they created, and still have Infestation on board to proceed to generate zombies post-board sweep.
Its a lot of cards, but the combo aims to draw and delay the opponent's game anyway so it can work. Fan Bearer and Cryptbreaker add additional zombie support and card draw/tap and Verity triggers.
Tomebound Lich seems pretty so-so, I'm not sold on it. Opt is in for now, but like I said Grim Tutor may be the winner here, I have to try it.
Edit: Lurrus of the Dream-Den would probably be good here!