Ball joints, tie rods and/or the steering box are your next culprits. That alignment may be suspect too.

If they have never been replaced, the joints are probably due for it. They should not have done and alignment if they were worn. The steering box has some adjustment in it that you can tighten.

But, if it is drifting around that much, I would suspect either the tires or the alignment. Rotate the tires and see if it goes away. Some brands of tires are just not that great. Are they fully inflated?

Go back to, or find one, an alignment shop and tell them your problem. Maybe they set something up out of wack. It happens. If it is in spec, then have them try to adjust it such that it should not do what it is doing. Caster and toe are two important things for keeping the vehicle pointed in a straight direction and for the tires to return to center. Maybe they can fix it that way. At the least, have them give the front end a good inspection.

Good Luck,
Michael