Never heard of that metal flap falling into the tank, but even if it did it wouldnt affect your fillup speed as it would just sit on the bottom of the tank it also wouldnt pass the filter in the tank,
Whats probably more likely happening is your vent tube on the filler neck has probably become plugged with something, usually a small flake of rust, the dealer will blow it out with compressed air and charge you $200 or you could get a private mechanic to do it for very little charge if no no charge at all.
Heres a pic of your filler neck,the small tube attached is the vent tube, if its plugged up the pressure in the tank will rise and shut off the pump