I'm late to this one but in case anyone ever reads this again I would suggest loosing the heavy armour and Maces on the Dregs.
Dregs should be tagging along just behind the zeds, shooting off arrows as they go, then rushing in to stab anyone the zeds have knocked to the ground to gain kills.
The Vampire only really needs a sword for parries and any other hand weapon. You then need to use it judiciously as it will kill lots but can easily be overwhelmed. Don't get into scraps with more than two opponents especially if one is a captain of some sort.
Finally I suggested dropping a load of stuff and this is a) to leave out superfluous kit you won't need but also so that you can b) buy and Ogre Merc. Ogres can be a bit meh on their own but they synergies so well witha vampire it's not true. Having another living M6 body is sweet but when it hits at S6 and sends opponents straight out the it can really help to keep enemy numbers down around your vampire.
Also if you can get sprint on your vampire, DO
IT!
Laugh as enemy snipers are charged down from 18" away! Undead are the best starter warband
IMHO.