Toe in should be set to almost straight head or you will have tire wear and other issues, 1/32 to 1/16 toe is ALL it needs. IIRC, that somewhere around .06 - .08 degrees. Take it back, make them center the steering wheel correctly and then check their numbers again. since they can't center the wheel correctly there is no telling what else they cannot read. I have gone thru multiple shops and multiple people at alignment places to get a CORRECT alignment, if you don't monitor them you do not know what they did right or wrong.
GoodYear does in fact make tires that are not rated for these trucks hence my suggestion you actually CHECK what you got for tires. If they stuck a set of C or D rated tires on there you are fighting a loosing battle. Trusting a tire shop is like trusting a dealer to do the right thing, check every single thing they do or you will have issues. As far as that goes Good Year is right up there with BFG being junk tires for these trucks, they never work out and always issues of some kind.
Tire squirm, if it does exist, should be so minor that doesn't effect anything. I have gone thru Toyo, Nitto, Falken, Cooper, and some others in various flavors on multiple trucks. If you have a good tire, it is rated correctly, and inflated correctly squirm doesn't happen. I have made shops replace the tires if it did not feel right and when a good tire is used there is no problem.