Unsolved brake pedal vibration -not rotors

[tringo007]

Hello, USA 2008 Toyota Yaris with no ABS (confirmed with toyota & mechanics) . Brake pedal pulsates / shakes when pressing on brake from 1/4 way down to bottom (mostly) when car in motion and when car is completely stationary. No impact on steering or anything else, ONLY the pedal. Happens about 75% of the time. Brakes hold fine, do not feel spongy or anything else.

WHEN I press hard on brake from 40-60mph down to 0 (almost locking wheels) braking gets perfect (no pedal vibration) for at least a few mins afterward until brakes get cool again then pedal vibration resumes.

The shaking is pretty significant and you can even hear it from the
passenger side. Following done to no avail:

1) Changed rotors (no improvement)
2) Changed brake booster, and all valves, connections etc into brake booster (no improvement)
3) Changed Master brake cylinder, diaphraghm etc and im assuming fluid when this was done (reduced intensity of shaking for a short time but then got bad again)
2) Checked wheel lug nut torque
3) Checked brake caliper & caliper bracket mounting bolt torque. Torqued mounting bolts inspected for wear, looseness etc. including worn mounting brackets, bushings and sliding pins.
4) Checked wheel bearing for looseness.

Toyota/mechanics cannot figure it out. What could be the problem?

Thanks..

Rene