as a retired ITC guy I read a lot of posts but yours prompted me to register. I don't know what kind of suspension you have under your E-350 but I have the twin I beam front end with king pins. All your caster is in the king pins - caster gives you the on center feel you are looking for. if the king pins drag you lose the benefit of the king pins caster. When you hit a bump with one wheel the truck wioll feel like it is stering out from under you. The first step to take is grease the king pins - From the sound of it you probably have never done this so it may be hard to get them to take grease. I f you prevail it will solve your problem - guaranteed.
You may need the other components everyone is talking about ( except for the ball joints) but grease alone will be a magic cure. Sometimes there is too much advice.