The thicker the case neck the smaller the inside diameter will be when it is sized before the expander passes through the neck. Then when the expander passes through the neck the thicker neck will have more spring back.
You say you had .004" difference, BUT if you remove the expander, and size the case how much smaller is the neck before expanding. If its .005 or more you may induce runout during sizing with a bushing die.
Below is my Redding neck thickness gauge and it tells me more about the quality of the brass than anything else.
In the gauge below is a Remington .223 case with .004 neck thickness variation between .010 and .014. Normally .223/5.56 cases have a neck thickness betwen .011 and .012 and you want cases with much better uniformity. Cases like this are not worth doing any prep work to and are used as blasting ammo in my AR5 rifles.
Bottom line, you need good brass before even thinking of using bushing dies and neck turning. And there is nothing wrong with just using a standard full length die.
I have bushing dies but get much lower neck runout using Forster full length dies with their high mounted expander that greatly reduces neck runout.
Below is a RCBS full length die that I equipped with a Forster expander and spindle assembly. And this setup produces far less runout than a bushing die does.