Them's the brakes

Our 2004 MPV Van recently began applying its own brakes. After being driven for about 5 minutes it would begin to need more and more gas pedal to maintain speed. It did not take long to realize that the car was braking since lifting the right foot caused rapid deceleration and then a complete stop. It can pass, or ease up, after a while, and return again, but it is not safe to drive like this and it will surely ruin the pads/rotors. When testing the car to see if it is working properly before taking off I will place it in Drive and let off the brake pedal. If it moves without applying the accelerator it is not grabbing. I will even test again by moving it to Neutral and watching the speed as indicated. If there is not a drop it is still moving freely. The brakes/calipers will close with no pressure on the pedal. As an example I have tried to drive it to a mechanic and while on the freeway done the Neutral test and then resumed driving (never touching the brake pedal) and the brakes apply by themselves. I have had the local Firest*ne dealer look at it three times and Mazda dealer twice. In order the responses were: FS) --- there is no problem. Mazda) --- there is no problem. Mazda) --- front caliper sticking. (Both calipers replaced) FS) --- I don't see a problem but maybe your rear pads are sooo worn that the piston/pistons are far enough out that the cylinder lip is catching and not allowing them to retract or bad/damaged hose. (New rear calipers and pads were installed) FS) --- It is the ABS pump. (ABS fuse pulled to remove ABS module from the equation) Problem continues. Firestone was used for three reasons; the problem occured nearest to them, they were open and they were aware of the problem. Have not taken the next step as I don't relish the thought of spending $1,200 plus labor on another guess. The only parts not replaced seem to be the ABS pump, brake booster and the master cylinder. Any insight would be greatly appreciated as in this situation my screen name does not apply (unlike my brakes). Respectfully I thank you