Mile High JDF is correct. You most likely have a caster angle problem.
In simplified terms, caster angle is the relationship of your tire's contact patch to the steering axis. A good mental picture of this is to think about the front wheels on a typical supermarket shopping cart, wherein the "contact patch" of the front wheels quite obviously trails the steering axis as you push the cart forward.
Increased caster = better straight line stability (less propensity to "wander") and more "self-centering" of the steering. . It also makes the tires lean into the corner when turned, in effect producing more negative camber when the wheels are turned. This allows you to use less aggressive Negative-Camber settings, thereby improving the tire contact patch for better braking and reduced tire wear when the wheels are straight.
On a New Edge Mustang running all stock parts with the strut towers not deflected out of whack from 11 to 15 years of life on the road, the stock caster angle is about 3.6 degrees; about 1,75 degrees on an SN95. That increase in caster angle from the 98 models to the 99-04 models is an example of Ford engineers responding to their customers, in a sense, because the stock castor angle on a Fox body was something like 1.25 to 1.7 and those of us who where road racing and autocrossing the things would run adjustable camber / castor plates with the max caster we could get, which was around 3.1 to 3.4 degrees. Ford simply built that in from 1999 to 2004.
There is just one teeny-weenie little problem, though.....
Unless you're running adjustable camber / castor plates, the castor angle isn't adjustable. This is one reason why I believe the addition of adjustable camber / caster plates should be one of the first mods made to these cars. The strut towers are almost sure to not be in the same OEM, "factory fresh" relationship with themselves and the rest of the unibody structure after a decade or more of road duty.
While you can have too much castor angle in theory, the reality on a New Edge equipped with adjustable camber / castor plates is that you can't get too much of it. When I set this, I don't even bother measuring it. I just push the tops of the struts as far back toward the rear of the car as I can get them. In doing that with the adjustable plates I run, the end result will be somewhere between 5.0 and 6.0 degrees. It's one of those "It is what it is" kinds of things and will be a little different an each individual car, but it can't be too much in the absence of major sheet metal surgery to relocate the strut towers on the unibody.