Pickup polarity and amp topology are very different concepts - the "push pull" amp design you're talking about doesn't really translate to the polarity of the magnetic poles in a pickup.
The polarity of the magnets determines the direction of the current in the windings. But the relationship in polarity among the poles on a given magnet also have a heavy influence on the shape and strength of the magnetic field. When designing a pickup, our goal is to "project" the field up towards the strings so they can be sensed. It's easy to mess that up when you start doing things like including north-up and south-up magnets or poles in close proximity in a single pickup. When nearby poles are all oriented the same way, the field lines tend to point straight up, away from the poles. When you have opposite poles near each other, the field lines tend to point straight from one pole to the other, and - depending on the overall arrangement - you sort of "miss" the strings.
There are some pickups where polarity isn't uniform. Notably, most humbuckers built with two coils next to each other (as in a typical PAF style guitar humbucker) have one coil with north up and one with south up. The design of the pickup tends to cast a wide magnetic field and still catches enough of the string to work well. That wide field is a big reason why humbuckers sound they way they do, compared to a single coil with a narrower field. If you look at a PAF design in a magnetic field simulator, it shows a really interesting field shape. If you do a cross section that's on the same plane as a given string, you find that - up where the strings are - towards the neck end of the pickup the field is strong. Then it gets very weak in the middle of the pickup, and stronger again on the bridge end. The design is basically sensing two areas of the string, just above and just below the two rows of pole pieces.
Another common design that uses both polarities in a single pickup is a split-coil Jazz pickup. These feature two smaller coils in line with each other stuffed into a normal jazz shell. Each coil senses two strings. The two coils typically have opposite magnetic polarities so they they are hum cancelling (when wired together with reversed wind directions as well). Split coil jazz pickups often have a dead zone right in the middle. If you put the design in a magnetic field simulator, you can see why - in that area between the two coils, the field lines are really strong down inside the pickup, but weak in that narrow swath up where the strings are. If you built a pickup with two poles per string and had the polarities of the two poles alternating, you'd basically be building a mini version of that dead zone directly in line with each string.
Your goal of having a sensing range that extends wider past the outside strings isn't a bad idea though. But there are good ways to do this besides putting two opposite polarity coils right next to each other. For instance, put two same-polarity poles next to each other! Like Leo did with J and P pickups. This gives you a wider field (side to side) AND a field that projects up towards the strings better. It's really the ideal design, compared to a typical guitar humbucker with a single pole right below each string.
A pickup with more poles than strings, and poles spaced more widely than the strings, has been done from time to time. Bill Lawrence did it with some of the Wilde pickups.
