The Romero zombies don't stop moving until their head receives significant damage. So perhaps we should treat them as ghouls that only take damage on a critical hit? Also, it doesn't seem to matter how the person died in regards to when / if they become a zombie. One character in the film was bit very slightly and mostly recovered. A few weeks later she died giving birth and arose a few seconds later (1d4 rounds) as a zombie.
That suggests a curse rather than a disease. Make it so that a successful bite requires a will save (DC 25?) verse a curse that will cause them to become a zombie after death. Along with this, add in a disease factor with a lower DC that weakens the person, eventually causing death. Perhaps DC 15 vs 1d3 Con and 1d3 Str each day until two saves are made in a row? Most typical first level NPCs and even some PCs will fail the save. It also has the factor that if someone gets ill and receives Remove Disease, they think they are safe from becoming a zombie. Nearly all first level NPCs and PCs will fail the curse portion, however. It might work even better if the DM requires the PCs to give their saves info before the game - then secretly roll the zombie based saves himself (and ask them to roll other saves). It may take them a day or two of game time to realize that the Con / Str damage is not automatic upon being bitten (due to a hunk of flesh being torn out, or whatever).
Giving zombies - or a ghoul variant - a disease that weakens, a curse that spawns and is hard to break / detect (maybe give the curse some SR?), DR vs non-critical damage (say DR 10 / critical or magic), +1 HD over the base creature (to give them more lasting power, or maybe max hp instead: 12 for 1 HD NPCs, etc), and a tendency to move in mobs rather than individually, and you have a really really dangerous undead creature. I think that EtR was trying to do the same with the Strahd Zombies (basically 6 HD dieased zombies), but it was not quite done in a way I would have done it.
In a low(er) magic world, the above could be terrifying. Especially if the SR against detecting or removing the curse was well played out. If it could not readily be detected there may be several areas that believe they are safe - until the chance cursed individual dies by some natural means or of the disease and bites a few others near by.