More for competitive fun rather than cutthroat. There is a lot of Blue Zombies that Mill my own deck like Laboratory Brute that I was hoping to work around as well. But I can't seem to grasp a good way of playing off that.
I run a zombie tribal deck (Lord of Tresserhorn, and you can find the primer in my signature. Although my deck has red in it, you will find a lot of the same cards you could expect to find in a blue/black version.
Tribal decks will typically not be cutthroat, but they can be competitive. My list is pretty competitive, but it folds against truly cutthroat combo or control decks.
I liked the ability of Gisa and Geralf letting me cast zombies from my graveyard rather than exiling them. I know it's only at my upkeep, but pairing that with Havengul Lich and Rooftop Storm makes a good combo. I also like the Dimir influence and find it cool to mill my opponents using zombies, but just not quite sure how to implement it.