Bottom line up front: Take fear causing heroes to combat autobreaking. I like the scarvet/cold one hide/lore of beast combo but don't forget that similar bonuses come from a scarvet with spear on a cold one!
Yeah, if you can get a fear causer in every unit that would be great. I would even suggest running some skrox units for just that reason. I think your priorities should be:
1. Fear Causers
2. Something to snipe vampires with
3. Static combat res
Fear causers in every unit (or even terror) will keep you from autobreaking when outnumbered. If you can kill off his vampires then he can't resurrect any more undead and the magic phase is yours! See if you can challenge them or shoot them with something. EotG works for destroying his units but the saurus with cold one hide/Lore of beast combo should work well in challenges. Bane heads or some other form of sniping which you can use reliably should be good too.
I understand that undead are immune to psychology but static combat res is hugely important against VC. It prevents you from autobreaking from fear causers and they take casualties when they lose combat. If you take one or two big blocks of 15 or 18 saurus plus some support units (skrox would work great for this) you'll deplete his units fast. Lizardmen support units are what win games, in my oppinion, so put an emphasis on them. That EotG which walks around blasting his units while your saurus grind them down from the front will soon find those vampires by themselves.
Okay, I understand many people dislike skrox units but they can generate amazing combat res against zombie units. They are only strength 2 or 3 right? Skinks might be able to actually stand up to them, not to mention the obligatory kroxigor or two. Even 11 skinks with a kroxigor can generate 8 combat res (+2 for ranks, +1 for standard if you take one, +1 for outnumber if you get it, +1 for flank, +3 net gain due to their loss of ranks plus or minus any casualties). That's HUGE. Add that to whatever your saurus block gets and you're going to massively win combats.
Try to use skinks/terradons to draw away parts of his army. You should be able to match him in the magic phase and the shooting phase should be yours. You just need to outmaneuver the horde of undead to win.
Let me know if this was helpful, thanks!