I had a similar idea for making a variant HMHVV "Romero Strain", although I wouldn't have it reanimate corpses. Instead, the regular virus would've mutated to act like a form of rabies, infecting normal people and turning them into ravenous cannibals. The virus would also have aspects of flesh-eating disease, causing necrotisation of the infected's flesh, and a numbing of pain, thus explaining why the "zombies" would look like corpses and be resistant to injury.
Mind you, the tissue necrosis would inevitably cause the "zombies" to collapse and decay, so they could be relatively easy to deal with by containing them until they collapsed on their own.
...Which would make a lot of Mega-Corps interested in their weaponization potential.
Edit: Alternatively, a Magically mutated variant of
Toxoplasmosis could work as well, as it's real-world counterpart has been known to induce Psychiatric Disorders in infected patients.