When making my request for a specific type of zombie game, I had no idea that there was in fact an entire web site devoted to that genre. So I went through and tried a whole bunch of them to see if what I was looking for already existed. Short answer: no. But some of them were close.
Boxhead: The Rooms
This overhead arcade game pits you against and endless onslaught of boxy zombies. You run around collecting ammo, blowing up barrels, and unloading whatever you've got into the zombies slowly lumbering towards you. The weapons are fun (and upgrade over time), but the selection mechanism for them isn't as precise as I'd like considering how fast the action is. The pacing is nice, with it never being too boring nor becoming entirely impossible. It also keeps driving the action forward with a combo system that requires that you chain kills together to keep your score up. This game also has one of the key elements of my ideal zombie defense game: traps. My main complaint is that you're only worried about your own skin; there aren't any other survivors or a base to defend.
Boxhead: Halloween Special
A variant of the Boxhead game above, this one requires that you rescue survivors instead of just holding off zombies by yourself. Which sounds like what I'm looking for, except that it seems to have come at the price of the fun frantic pacing of Boxhead: The Rooms. It takes awhile before you really have to worry about the zombies at all. And fundamentally the slow helpless survivors are a pain to escort (they're definitely part of the problem, not the solution). They're not really interesting to guide either, as that you always pick them up and drop them off at the same locations.
This is another arcade survival game, except this time you also have a base to defend. The base isn't more than a little bunker, but it makes holding off the zombies more interesting. Do you let them go for the base and stay out of harm's way? Or do you risk your own neck to bait them off the base? Similar to The Last Stand the zombies come in waves, and in-between waves you can repair the barricade and get new weapons. Unlike The Last Stand there are no other survivors to help you with base defense. However there are far more options for how to upgrade your character. You can increase your movement speed, decrease your reload time, and choose from a much wider selection of weapons (including a minigun and a laser cannon). The pace of Zombie Rampage is way too slow at first (a common problem, and truthfully one that S&I had as well), and the terrain isn't interesting in the slightest. Add some fellow survivors, a more interesting settlement to defend, and some reasons to risk venturing far from the base (supplies, other survivors, whatever), and you've got a contender here.
Zombie Horde 3
It's clear that this game has a lot more effort poured into it than the games above. There's a story with cut scenes, an intricate equipment interface, a mini-map, day/night cycles, and vehicles. But it's amazing how with so much time spent on development, not a lot of thought went into the game's pacing. Before you can advance the story you need to buy a new weapon to break into the police station. Raising that money involves wandering the city killing zombies for cash. Unfortunately the city is completely barren, and the zombie spawn rate is terribly slow. A couple minutes in and I was already bored. Combat was infrequent, and when it did happen it was easy. I finally got enough money to buy a shotgun and break down the barricade, but after a short story sequence I randomly got cornered by many more powerful zombies and quickly went from bored to dead. Game over.
I hate to be so harsh on this game, because the infrastructure is high quality. Equipping your character looked compelling, I like that you get a melee attack, and the nighttime flashlight effect is nice. But being technically competent does not make a fun game. The save system ensured that I didn't lose too much time, but after dying I really had no motivation to keep going.
Guess I'll have to keep looking...