I've had to roll up my sleeves a number of times on my 2005 also.
The charcoal canister shutoff valve can stick open or closed, either will create a check engine light. I've had mine stick open twice and closed once. It sounds more like stuck closed, but that's not really what happens. If it sticks closed you won't be able to get fuel to go in at all, well it will take like 10+ minutes to feather the pump slow enough to get it to fill, put it that way. You got a check engine light on? I assume you'd mention it.
If it sticks open, refueling will be normal as it is supposed to be open at that time anyways (key off).
So I think it's something else. Just not sure what. Will it do this at any gas station? What if you don't set the fuel pump handle at full speed?
One thing I have learned is one the pump clicks off, don't go any further as this is what messes up the shutoff valve. You say it overflows and the pump handle never clicks off or it does but it's too late to prevent an overflow? Weird problem. Mine has almost never done that, maybe twice in 10 years of ownership. What cab does yours have the filler tube is a bit different on the crewcab (different filler location), may be a different tube.
2017 Crew Cab Long Box Z71 V6 4WD Brownstone