On mine, once I determined that the hard start was repeatable after every fill up I figured that the engine was getting flooded with vapors from fueling.
I dug into my manual and found out that there is an EVAP Canister Purge Valve. Basically it's a PCM controlled solenoid valve which controls vapors to the intake. The valve is normally closed and then the PCM will tell it to open after the engine is running to consume the excess vapors from the EVAP canister.
When mine failed, it failed open so that the vapors had a clear path to the intake and flooded the engine during each fueling.
It basically has 3 connections. Vapor inlet from the EVAP Canister. Vapor outlet to the intake and then the electrical connector. You can test the valve with a meter to determine condition, but off the top I can't remember whether you'll have continuity or not. However, I do remember that the new one I ordered had the opposite condition which gave me some confirmation. The true confirmation came the next time I fueled up and the engine started right away and has ever since.
The valve can be accessed from the doghouse side and if I remember correctly is was on the driver's side of the motor.
Motorcraft part #s
Obviously YMMV, but this worked for me. FYI my van is also a 2005.
2005 E350 4x4 V10