Oh man, I feel like a pig in shit right now. Just found what I've been looking for for ages, a good ArmA single-player offline endless survival mission.
It's got zombies, but they're slow walkers instead of the lag nightmares, so they really serve to build that mounting pressure to keep moving (instead of just randomly killing you and running through walls). It's got AI survivors, bandits, &c. so you've got real enemies to fight, but they're tuned to a sane difficulty level so you don't have entire groups drilling your head with assault rifles from 1km away as soon as you poke around a corner. It's got no other players (obviously), so most of the time when you hear a shot it isn't right as you die because a bush wookie in a tree on a hill almost beyond your draw distance decided to waste a bullet on you in particular. No annoying server restrictions or risk of a server going down. No lag.
In 30m I had a better experience than I've ever had online. Spawned east of Cherno, wandered in, scavving the outlying little clumps of buildings. Found a wrecked humvee by the chapel. Wasted half a mag of Makarov on a zombie. Started looting up Cherno, but the zombies accumulated and I ended up dashing away from what I was doing through a semi-open field. Shots started cracking around my head, but I didn't get hit. I made it to a wall and heard more shots not directed at me. Kept looting on the run while making my way west. On the way out of the city towards the forest I got shot at again from extreme range. Once I was in the trees, more shots inside the city (presumably the AI was getting pressured by the zombies I'd left behind).
Made my way further west toward the southern airfield, found an open-topped Ural and repair kit on the way. I killed a couple nearby zombies with the M9 I'd found at some point, fixed it up, and started driving in the same direction, then I saw a group of three fully geared AI moving south across the airfield, so I swerved north into the forest (thankfully without being spotted) and holed up in a little hamlet, which is where I saved and left.