Not Army: Industry:
A bit of a frame shift. Your zombies aren't behaving like an army, or fighting a war. Instead, they are behaving like a force of nature fueled by human population.
- Harvesters: Use agricultural machines. A harvesting machine is built to feed in lots of matter, chop it up and blow the bits out or under the machine. With a few modifications, they can be converted into zombie manglers. A Zombie chopped into a hundred pieces might still technically be a threat, but good luck with them getting you. Soon your harvester is like a tank - invulnerable to zombies, chewing them up, running them over, and driving back to a cleaning facility to be disinfected and refueled. Hey, is that an elbow moving?
- Traps: Similar to harvesters but less mobile. A set of chutes offers zombies an easy path towards obvious prey. But a set of chainsaws or rotary saws systematically slices the zombies into thin sections which are then dropped into an industrial meat grinder. A person on a motorcycle drives around, aggro's a bunch of zombies, and leads them to the factory. Or feed lot. Or saw mill. Now what to do with all the zombie paste?
- Biology: Okay, at some point, these things will start to break down. Whatever is making them go can't completely change chemistry. So start culturing bacteria that break down dead human flesh. EEWW!!! Well, not half as gross as being eaten alive. The zombies must be partially liquid (or they'd stop moving) so they would be susceptible to accelerated rot. I'd suggest crop dusters. Now necrophagous (corpes-eating) flies and beetles are bred and dumped in high density areas and the zombies are being digested, used to breed maggots, and surrounded by blinding, buzzing insects everywhere they go. Once the zombies are infected and the insects are spreading, they will go along with the zombies (the food source) and digest any fresh zombies. If the zombies do nothing, they're bug food. If they swat the things, they're going to be preoccupied with not being eaten. Poetic justice, no?