Yaris brake problem-not rotors

Hello, 2008 Toyota Yaris (no ABS) brake pedal pulsates / shakes only when pressing on the brake up to about half way down. No impact on the steering or anything else, only the pedal. Brakes hold fine, do not feel spongy or anything else. It happens more when engine is warm and happens when car in motion AND when completely stationery. It also does not happen with every brake press when engine is warm, but about half the time. The shaking is pretty significant and you can even hear it from the passenger side. Following has been done to no avail:

1) Changed rotors (no improvement)
2) Changed brake booster (no improvement)
3) Changed Master brake cylinder and im assuming fluid when this was done (reduced intensity of shaking slightly)
2) Checked wheel lug nut torque and tightened evenly to specification.
3) Checked brake caliper & caliper bracket mounting bolt torque and inspected for looseness. Torqued the mounting bolts and inspected for wear or any looseness, including worn mounting brackets, bushings and sliding pins.
4) Checked wheel bearing for looseness.

Champion Toyota said it happens with some toyota's when diaphragm shakes and it is perfectly safe and fine to ignore but i did not accept this and after complaints they changed master cylinder and brake booster to no avail and they do not know why problem still exists. They do not know what to do next. Also carried to independent mechanic who cannot identify cause after checking everything. What could be the problem?

Thanks..

Rene