I've had a couple of stuck accelerator pedal screws to deal with in the past. The solution is sort of easy. Make sure you have a replacement screw before you try this. Also keep in mind that there is a spring nut on the end (right hand side) of the screw that may or may not be the removal problem or even be there.
Pop the hood; remove the accelerator arm to the carb; remove the three 14-10X5/8 hex head sheet metal screws that attach the accelerator arm pivot to the firewall; back inside, flip the arm for access to the Phillips screw; use ANYTHING to get the screw out - vice grips, hacksaw, Dremel, words - etc. You can figure out the rest.
Oh, and thank the automobile gods there is no computer in a 1965 Mustang - (or offensive carpet either).