Front End Floats

Rusty and AJ have it right.

If you took the car to a major chain alignment shop it's aligned to factory specs, which are garbage. You need almost exactly the opposite of what the factory called for, because the factory specs are for bias ply tires. Radials should have negative camber and positive caster. Specs vary a bit depending on application, but if you can get -.5* camber, +3* caster (or more if possible) and 1/16 to 1/8" toe in you'd have a good start.

Wandering is usually toe, caster, or tire wear. Wiped out tie rod ends or suspension bushings can do it too. Sway bars won't help at all for wandering. A worn out steering box can make wandering feel worse, but it's not the cause.