+1 on the tuner and elmination of limiter, and yes lowering the car makes a huge difference as does the other supporting suspension mods. Not only does the car handle tighter and a bit more nimble, but you cut the wind from beneath the car which makes for a significant stability increase as opposed to the 4x4 height. When travelling at these type of speeds for long durations of time, in these s197 platforms it's a host of things that really are making you get the sensation your feeling.
i didnt want to postwhore.
get a tuner and turn off the limiter. they are set to limit at 143, IIRC. speedo error, tire wear, viewing angle of the gauges, etc. could have caused the slight difference between what you saw on the speedo and where the ECU limited speed.
also, as mentioned already aerodynamics play a huge part in handling at those speeds. in case you have not heard, the S197 is not as aerodynamic as the new edge stangs.
I didn't bother to read most of the posts however I understand that you have factory ride height. Lower it and it will feel more stable, Ford cool their radiators from air coming underneath the bumper by the front valance (thats why so few holes in your grill) that causes the nose to lift. I had mine to 120mph at factory ride and scared the balls off me, after lowering I got to 130 and she was stable!!
The FRPP handling package comes with camber eccentric adjustment bolts so you can set the camber to proper specs...It doesn't specify in instructions but they have to be installed on the strut the opposite way the factory bolt came off (easier to adjust) which requires removal of the brake caliper off the rotor. It took me 3hrs and I'm a spaz with 10 thumbs....my employees were keeping a close eye on me with wrenches ready to jump in.